03 TR]BHUVAN UNIVERSITY

INSTITUTE OF ENGINEERING
Examination Control Division
2075 Bhadra

r' Candidates are required to give their answers in their own

words as far as practicable'
r' Atrcmpt All questions.
r' The jguris in the margin indicate Fall Mark'
/ Assume suitable data if necessary.

1'HowforcedE.Moscillationissetup?Writethedifferentialequationwithitsso.lution.of
suchoscillation.AndhencediscussaboutresonancecurveandsignificanceofQual'tY',.
factor. ' '.|'2+21

2. A mass of I kg is suspended from a spring of spring constant 25N/m' If the undamped

fie4uency is the damped frequency, what will be the damping factor? tsl
{times
,VJ

is c.m. The Block's

3.
- At t = 0; the displacement x(0) of the block in linear oscillator -8-50
vetocity v(0) then is -0.920 m/s and its acceleration a(0) is 47 r/s2' Find
a) Angular frequency b) Phase constant 125+2.51
for, thc
4.' How Newton,s Rings are differ fmm Haidinger fringes? Derive an expression
you obtain central ftinge dark in
diametel of bright rings in transmitted light. How can
this system? ll+3+11
OR

Definediffractionoflight.showthattheintensityoffirsimaximaisl22ofthecentral
maxifira. [1+4]
given wedge angle'
5 . Show that fring€ width of wetlge shaped film is corstant for a 151

retardation O will
6. A Quarter wave plate is meant for fo = 5'S93 x10-s cm' what phase
show for L = 4.358 * l0-5 cm? Oleglect changes of pa and p" with 1') t5l

'-
T.Definecardinalpointsofacoaxiallenssystem'Findtheeguivalentfocallengthforthe
of two coaxial thin lens of focal lenglh 'f" and 'fz' separated by a
"o.iinutioo
distance'd'. Q+31

-
8. Discuss the significance of numerical aperture (NA)' How does it depend on
index of cladding and core? L2+31

g. How Gauss law is superior than columb's law? Show that the electric field
on the axis of
-' field an infinite plane of charge
u *iro.rnty charged disk is equal to the elecaic near
case. U +41
limiting
10. Show that the motion of an electron constrained to move along the axis of a thin non
rlng of radius 'a' uniformly and positively charged with linear charge density
l, is simpie halrmonic if it is displaced a small distance 'x' along the axis (x<<a) and
"ooau"tirrg
released.'Hence fintl the oscillating frequency. t51

OR

AcapacitorofcapacitanceCisdischargedthrougharesistorofresistanceR.Afterhow
many time constants is the stored energy ; ofits initial value? I5l
 11. Prove that the capacitanc€ of a concentric spherical capacitor of radii a and b is
, C = 4mo[b2(b-a)]. If outer plale is charged positively and inner sphere is earthed. tsl
12. A copper wire has cross-sectional area3.3l " 10-6 m2 and carries a curent of I0 A. What
is the- Orift speed of the electrons? (Density of copper = 8.95 gnr cm-], Avogadro's
number Nn = 6.02 * l02l mol'|, molar mass of opper = 64 gm) t5]
13. A circular parallel plate capacitor ofarea 154 cm2 is being charged has a uniform ctment
density of a displacement cunenl having a magnitude 20 Nm". Calculate
(a) the magnitude of magnetic field at the distance r = 50 mm aborfr tlrc oentral axis
between the plates. (b) dE/dt in this region [2.5+2.s)
14. With necessary circuit and graph, derive aa expression for rise and frll of csrrent in LR
circuit. Hence explain the inductive time constant for this circuit. [2+3]
OR
What is cyclotron? Show that the maximum energy of the ion in cyclouo is directly
proportional to the square of the frequency. [l+4]
15. Sunlight strikes the earth outside its atmosphere with an intensity of2 Ca!/cm2-min.
Calculate the magnitude of electric and magnetic fields. I5l
16. Using Schrodinger wave equation, calculate the values of the energr of a gticle in an
one-dimensional infinitely deep potential well. Indicate graphically tfre firl duee wave
function for such a particle. [3+21
++*
 TRIBHUVAN UNIVERSITY
INSTITUTE OF ENGINEERING
*
Examination Control Division
2075 Baishakli

Subject: - Engineering Physics (SH4S2)

,/ Candidates are required to give their answers in their own words as far as practicable.
/ Anempt AII questions.
r' AII questions carry equal marks.
{ Assume suitable data if necessary.

1. Derive the resonance condition in an LCR circuit. Briefly explain the quality factor and
hence show the quality factorwill be higher if the band width of the circuit is lower.
2. What is Ulfrasound? How these waves are produced? Write the fields of major
application of Ultrasound,
3. Show that the wavs equation of a fiansverse wave in a string is

+
dx2= 44,*noe
v2 dt'
v= ,,E , where F, = mass per unit length
1r,
4. Explain howNewton's rings are formed and describe the method for the determinations of
refractive index of liquid using Newton's ring formula-
OR
Discuss Fraunhoferdiffraction due to a single slit. Draw a curve indicating distribution of
intensitf of diftaction patterns. Is there any fundamental difference between interference
and diffiaction? Give the reasons.

5. What is double Refraction? Explain how Nicol prism can be used as polariser and
analyser?
A difftaction grating has 4000 lines per cm and is used at normal incidence. Calculate the
dispersive power of the grating in the third order spectruur for the wavelength 500nm.

7. Write down the charactedstics of LASER and its use in holography. How semi conductor
laser is produced?

8. It is desired to make a converging achromatic lens of mean focal length 30 cm by using

two lenses of materials A and B. If the dispersive powers of A and B are in the ratio l:2.

9. ;H"::,tJffi".f;T#,::'j;cnerdduetoaninnniterineorch*;.
OR

What is dielectric constant? Prove the relation 6 = eo E+i, Where slmbols carry ttreir
usual meanings.
10. Two tiny conducting balls of identical mass m and charge q hang from non conducting
thread each of length L. Derive and expression for the equilibrium separation rx' between
the balls assrmring that the separation angle to be small.

OR
What is a damped em oscillatiors? Which factor in the circuit is responsible to produce
such a motion? Derive a differential equation for this motion and write its solution. What
will be the remedy of such motion to make it smooth?
*
11. A parallel plate capacitor contains two dielectric slabs (of equal dimensions) of dielectrics
Kr and Kz as shown in figure below (i) Find the capacitance in each case if A is the area
of each plate. (ii) If Kl : 2 and Kz = 3, what will be the ratio of the capacitance in two
cases.

12- Ap.d. of lV is applied to a 30.5 m length of copper wire (diameter 0.02 inch). Calculate
(i) The current (r1) Cunent density (iii) The electric field strength (Given, Resistivity of
copper is l.7x I O-tCl-).
13. Discuss the Hall Effect. Derive (i) Hall voltage (ii) Hall coef;ficient and (iii) Hall
resistance. Explain that the Hall resistance leads to the quantum Hall effect.
14. Derive an expression for the magnetic flux density inside a long solenid, carrying current
l, at apoint nearits center.
OR
Derive an exPression for growth and decay of current in inductance and resistance circuit.
Also explain the decay current in LR circtrt.
15. Prove that charge conservation theorem with the help of maxwell's equation of
electromagnetism.
16- Using the uncertainly principle, calculate the minimum uncertainty in velocity when an
electron is confined to a box having a length lnm. Given, m :9.lxl0-3t Kg,
h=6.6 x l0{aJs.
+**
 TRIBHUVAN UNIVERSITY
*
INSTITIJTE OF ENGINEERING
Examination Control Division
2n74 Bhadra

--Fv.!ie-"!::lLsl!es:iru-Bt':rst-w!sl)-
{ Candidates are required to give their ans$€rs in their own words as far as
practicable-
/ Attempt AII questions-
Allquestions carrY equAl marks.
r/ Assume suitable data if necessary-

1. Define centers of suspension and oscillation of compound pendulum and show that they
are interchangeabte. What length of the pendulum has its marimum time period?
OR

Derive a differentiat equation for LC oscillation. Show that the maximum value of
electric and magnetic energies stored in LC circuit is equal.
2. What are basic conditions for acoustics of buildings? Derive Sabine's reverberation
formula and also write its two importances.
3. A rod vibrating at lZLIz generates harmonics wnv€s with amplitude of 1.5 mm in a string
of linear mass density 2gmlm. If the tension in the string is l5N, what is the average
power supplied by the source.
4. Explain the circular nature of the Newton's interference fringes. Show that square of
ruAi* of the nth bright fringe of Newton's ring due to the reflected light is proportional to
Zn-t.
OR

Show that coherent light waves represented by equation Ex -: Er sin(wt+6)

Ey Ez sin wt

. Give rise generally to an elliptically polorised wave that can become linearly and

5. What is the highest order spectrum which may be seen with monochromatic light of
wavelength 600 nm by means of a diffraction grating with 4500 LineVcm.
6. Write the physical significance of dispersive and resolving power of grating. Also
establish the relation between them. '
7. What is population inversion? Explain why laser action cannot occur without population
inversion bltween atomic levels? Write a method for getting He-Ne Laser-
8. Two thin lens of focal length fi and f2 separated by a distance d have equivalent focal
length 50 cm. The combination satisfies the conditions for no chromatic aberration and
minimum spherical aberration. Find the value of f1, fz and d. Assume that both the lens
are the same material.
g. What is quadruple? Derive an expression of the electric field intensity at a point due to
quadruple at axial line?
OR

Find the expression for the electric field intensity at a point along the center perpendicular
axis of the charge disk and distance z from center. Extend this result in infinite charge
disk.
..^ 10. If copper coin has mass 3.11 gm, what is the total charge on the nucleus of the atoms in
t the coin? Also find'number of protons inside the nucleus. Molar mass (M = 63.5
gm/mole, Avogadro nurnber (Nn) :6.02x1023 atom/mole.
ll.Discuss a microscopic view of ohm's law and show that resistivity of a conductor is
independent of the external electric field.
OR
State and derive Ampere's law in magnetism. Why and how Maxwell modified it?'
12. A circular coil having radius R carries a current I. Calculate the magnetic flux density at
an axial distance x from the center of the coil. Explain how the coil bahaves for a large
distance point and at what condition field will be maximum?
13. Find the expression for maximum energy of a rotating panicle in a cyclotron. How
cyclotron is different from synchrotron?
14. An inductance L is connected to a battery of emf E through a resistor. Show that the
potential different across the inductance after time r is Vr-: B"{R/L)I. At what time is the
potential difference across the inductance equal to that across the resistance such that
i: iol2.
15. Write Maxwell equation in differential form. Convert them into intemal form. Explain he
physical significance of each of them
16. Derive Schrodinger time independent wave equation. Explain the physical significance
of the wave functions.
**:N.
 TRIBHWAN T.INIVERSITY
* INSTITUTE OF ENGINEERING
Examination Control Division
2073 Magh

,/ Candidates are required to give their answers in their own words as far as practicable.
{ Attempt All questions.
{ AII questions carry eqaal marl$.
{ Assume suitable data if necessory.

l. What is compound pendulum? Derive the expression of it's time period and discuss about
the collinear points in compound pendulum.
OR
Discuss about the damped electromagnetic oscillation. Find the expression for damped
frequency. Also discuss about over damping, critical damping and under damping
conditions.
2. In damped harmonic motion, calculate the time in which (i) its amplitude and (ii) iis
energy falls to lie of its undamped value if the mass of the system is 0.25 gm and
damping constant is 0.01 g/s?

3. Define reverberation time. Derive Sabine's formula for reverberation time.

4. Explain the formation ofNewton's rings in reflected light. Prove that in reflected light the
diamete?s of dark rings are proportional to the square roots of natural numbers.

OR
Describe how will you produce linearly, circularly and elliptically polarized light.
5. Two thin converging lenses of focal lengths 0.2m and 0.3m are placed coaxially 0.10m
apart in air. An object is located 0.6m in front of the lens of smaller focal length. Find the
position of the two principal points and that of image.
6. A glass wedge of angle 0.01 radian is illuminated by monochromatic light of wavelength
6000A falling normally on it. At what distance from the edge of the wedge, will the lOh
fringe be observed by reflected light?

7. Define acceptance angle in optical fiber. Show that, Numerical Aperhue (NA) : W J2L, ;
where p1 is refractive index of core of optical fiber, A is fractional refractive index
change.

8. Light is incident normally on a grating 0.5cm wide with 2500 lines. Find the angles of
diffraotion fcrr the principal maxima of the two sodium lines in the first order spectrum,
l"r :58904 and )"2:-5896A. Rre the two lines resolved?
9. Derive an expression for the electric field and at a point P at a distance x from a circular
plastic disc of radius a along its central axis. Does this expression for E reduces to an
expected result for.x>>a?

OR
Calculate the potential at any point due to an electric dipole. Hence, find the potential on
the axial line.
.,'* 10. A neutral water molecule in its vapor state has an electric dipole moment of magnitude
7.lx 10-30c-m. If themoleculeisplacedinanelectricfield af2.5x lOaN/C,(i)what
maximum torgue can the field exert on it? (ii) How much work must an external agent do
to turn this molecule end for end in this field?
11- Prove the capacitance of a concentric spherical capacitor of radii a and b is
C : 4neOfgl . If outer plate
r is positively charged and.inner sphere is earthed.
Lb-u-J
12. Differentiate between semiconductors and super conductors. Discuss about critical
m4gnetic field in superconductors. Also prove that superconductors are diamagnetic in
nature.
13. Derive the relation for rise and fall of current in LR circuit. Explain the graph
between
current and time and obtain inductive time constant in both cases.

OR
State Ampere's law. Find out the expression for magnetic field at a point outside, inside
and on the surface of a curent carrying conductor using this law.
14. What is self induction? Develop a relation for induced emf in a coil. Caiculate the self-
inductance of the solenoid having length /, number of turns N, area of cross-section A,
and current I.
15- A certain plane electomagnetic wave emitted by a microwave antenna has a wavelengttr
of 3cm and a mo<imum magnitude of ele ric field of 2 x l0a v/cm.
(i) What is the frequency of the wave?
(ii) What is the maximum magnetic field? and
(iii) What is the maximum energy density?
16- Prove that the energy levels are quantized, when the electron is confined in an infinite
potential well of width "a".
***

.)
*
TRIBHUVAN IjNIVERSITY
TNSTITUTE OF ENGINEERINC
Examination Control Division
2A73 Bhadra

(sH4s2)

Candidates are requred to give their answers in their own worCs as far as practic-.able-
Attempt /!!questions.
fl questions carry equal marks-
Assume suitable data if necessary.

1. Shorv that motion of a disk of a torsion pendulum is angulal harmonic motion. Find an
expression for its angular fiequency and time period of oscillation.
OR

What is em oseillation? Derive the differentiai equation of forced em oscillation. Flence

find its resonance frequency.
2. A mass of 2 kg is suspended from a spring of spring constant 18 N/rn. If the undamped
ftequency isZl lb times the damped frequency, what will be the damping factor?
a
J. The volume of a hall is 475 rn3, the area of the wall is 200 *t, are*s of the floor and
ceiling each is 100 cm'. If absorption coefficients of the wall, ceiling and floor are 0.03,
0.04 and 0.05 respectively, find the reverberation time for the hall.
4. Is it necessary thal the interf,ering waves should have equal amplitude? Derive an
expression for condition of constructive and destructive interferences for reflected light in
case of thin transparent film of uniform thickness.
OR

What are dispersive power and resolving power oi a diffraction grating? Show that the
resolr.ing power of a grating is proportional to the number of ordcr.

5. White light falls normally on a film of soapy rvater of thickness 5xl0-s cm ancl refractive
index 1.33. Which waveleng1h in the visible region will be reflected ntost strongly?
5. What are retardation plates? Find out qn expression to find the thickness of a retardation
plate that produces eliiptically poiarized light. '
t. Derive the expression for the equivaient focal length of two thin lenses haviiig focal
lengths fr and f2 separated by a distance d. Aiso find the position of principal points.
8. If the numerical apernlre be 0"244i arrd refractive index of core be 1.50, calculate the
refractive index of the cladding and aeceptance angle in an optical fiber.
9. What is quadrupole moment? Is it vector quantity? Derive an expression of eJecuic field
iniensity due to linear quadrupole at axial line.
OR

What is eiectric flux? Is it

scalar quantity? Use Gauss's law to find the electric field
strength outside and inside of uniformly charge distributed conducting sphere of radius R.
 10" capacitor f fluctuating
the
e that e T is givei
I dxl
-;dr j'
11. The super conducting state of a lead specimen has critic 6.2 K at zero
-magnetic field and the critical field is 6.4x104 Alm at 0 K critical tjeld at
5K.
12. An inductance L is connected to batterv of emf E through a reisistance. Show that the

inductor affects the growth of current i

(
: iol I e-rst)
\'1, o, which condition it reduces to
l.
l.)
0.63i0.

CIR
Derive an expression for energy stored in magyretic field. Show that the magnetic energy
density is directly proportional to the square of magnetic field.
13. A copper strip 2 cm wide and I mm thick is placed in magnetic field 1.5T. If a current
of
2004 is setup in the strip, calculate^(a) Hatl voltage (b) Hall mobility of the number of
elections per unit volume is 8.4x 1028 rn:3 and resistivity is 1.72x I 0's ohm-m.
l4' A parallel pllte.capacitor with circular plates is being charged by varying electric field of
1.5x1012 Vm'ls'I. Evaluate the induced magnetic field if the radius of the plate is 55 mm
and displacement current.

15, Write down the Maxwell's equations in free space and in dielectric medium.
With the
help of Maxwell's equations, derive charge conservation theorem.
16. An electron is confined in an one dimensional infinite potential well of width /, the
potential enersy is v(x) = i:L@ x<0andx>1
-t:::]- , Find the eigentuncrions

*c energy v^6v'Ysrrr!"
lr"(*)=agn[3"*J *-'" E -t]t!'
eigenvatues r-,n - -ffi'
t | )
:t**
 I
03 TRIBHWANUNIVERSITY Exam. Neu'Blcli (206(r & Latcr Batch)
INSTITI.J'IE OF ENGINEERING Level BE Full Marks 80
Examination Control Division Programme BCE, BGE, BME Pass ll{arks 32
2072}.[.tgh Yeer / Part ltil Time 3 hrs.

Subiect: - Engineering Physics /SH452)

r' Candidates are required to give their answers in their own words.as far as practicable.
r' AuemptAll guestions.
/ All.questions carry equal marks.
/ Asswne suitable data if necessary.

1. Differentiate between"linear arid angular harmonic motion. Prove that three exits forn
'. collinearlint ina barpendulum.
I
!

i
OR
I'
I Derive a relation for current floping in the circuit containing a resistor, an inductor and a
capacitor in series with a sinusoidally varying emf. Find the condition for current
I responce.
.

2. A sirrple pendulum of length 40 crn and mass 50 gn is suspended in a car that is

' haveling with a constaht speed 40 m/s around a circle of radius 100 m. If the pendulum
undergoes small oscillations in a radial direction about its equilibrium position, what will
I
! be its frequency ofoscillation?
''i

I
3. Write a plane progressive wave equation for a wave propagating along the *ve x-axis.
I' Prove. the following relations:
I
'I
I

I
i) Particle velocity at a point: - (Wave velocity) X (Slope of the displacement curve at
.l that point)
i

I
ii) Particle acceleration at a point = (Wave speed)2 X (Curvature of the displacement
j
l curve at that point)
I

4.
I

What is chromatic aberration? Show that longitudinal chromatic aberration is equal to (i)
,j
I
I coxf, when object is at infinite and (ii) 99, when object is at finite. Where symbols
:
f.1
have their usual meaning.
5. What are Newton's rings? How.can you determine the refractive index of given liquid
using Newton's rings experiment?

OR
Differentiate between quarter wave plate and half wave plate. Use the reference of double
refraction to describe with diagram, how you distinguish positive and negative crystal.
6. What is the difference between the resolving. and dispersive power of the planq
transmission grating? Show that both resolving and dispersive powers are directly
proportional to order of tfue spectrum.
7. A sugar solution in a tube of length 200 mm produces an optical rotation l3'. The
solution is then diluted to (1/3) of its previous solution concentration. Find the optical
rotation produced by 35 cm long tube containing the diluted solution.

L.
 --?r

i
,1
L
1,

8- An optical fiber has a numerical aperture (NA) of O-22- care has refractive index
,: rye of 1'33' Also,
1.60. Calculate the acceptance angie in water that has refractive index
calculate fte critical angle at core cladding interface' .
. g. Define electric dipole. Charges of an electic dipole are replaced by identical charges;
find the electric field and potential ar apoint on its axial line'
OR

Derive a relation for electric field at a point on the axis of a positively charged plastic
ring. Show that if an electron is constrained urithin the axis of ring, motion of electron
will be SHM.
10. If a disk of radius 2.5 cm has a surface charge density of 8.6 pClmz onits upper surface.
What is the electic field (i) at a surface of the disk and (ii) at a point on the central axis at
a distance 15 cm from the disk?

11. A parallel plate capacitor whose capacitance C is l3.5pF is charged by a battery to a

potential difference Y :
12.5 V between its plates. The charging battery is now
disconnected and a porcelain slab (k: 6.50) is supplied between the plates. (a) What is
the potential energy of the capacitor before the slab is inserted (b) What is the potential
energy ofthe capacitor-slab device after the slab is inserted?
12. A copper wire of cross-section area 3x10{m2 carries a steady current of 60,{. Assuming
one electron per atom. Calculate (r) free^elecnon density and (ii) average drift velocity.
Given, Density of Cu = 8.9xl0rkg/m', Molar mass of Cu = 64 and Avogadro's
Number = 6.02x 1023/mole.
13. Detennine the energy stord in an inductor. Also, determine the energy density in
' magnetic field.
i}
;t
: OR
Obtain an exprcssion for magnetic field intensity due to a circular coil carrying curent at
its a:dal point. Compare the result with that due to short bar magnet.
14. Suppose a cyclotron is operated at an oscillator frequency of 15 MHz a"d hgs a dee of
radius 55 cm (i) What is the resulting kinetic energy of deuteron? (ii) What is the
, magnetic field needed for deuteron to be accelerated in the cyclotron? Given: mass of the
deuteron = 3.34x I 0-27kg.
. 15. Write Mar<well's equations for non conducting mediumlUsing these equations determine
the electromagnetic wave equation in terms of magnetic field for a non conducting and
an-isotropic medium having fgnite permiuivity (p) and frnite permeability (e). Hence
prove that the velocity of electromagnetic wave is equal to velocity of light in free space.
' 16. What is the physical meaning of wave firnction? Derive the Schrodinger time
independent wave equation.
*+!t
 03 TRIBHUVAN I.JNIVERSITY Exam. Regular / Back
INSTITUTE OF ENGINEERING Level BE Full Marks 80
Examination Control Division Programme
BCE, BME,
Pass Marks 32
BGE
2071 Bhadra Year / Part Utl Time 3 hrs.

Sabject: Physics (5H452)

/ Candidates are required to give their answers in their own words as far as praclicable.
r' 'Attemp AA questions.
/ Thefigttres ln the margin indicate Futt Marks.
{ Assume suitable data if necessaryt.

l. Develop and solve the differential equation of damped harmonic oscillator subjected to a
sinusoidal force. Then obtain expression for its maximum amplitude and quality factor. tsI
OR
Obtain an expression for current in a driven LCR circuit and discuss how the current
leads or lags the applied voltage in phase:
a) When the net reactance in circuit is inductive and
b) When the reactance in circuit is equal to resistance. Illustrate it with the help of a
/1
figxe.
?/ A circurthas L - .z mH, C : I.6 pF and R = 1.5 O. (a) After what time t will the
V amplitude of, -narge oscillations drop to one half of its initial value. (b) To how many
periods or --dlations does this correspond? t5l

2 of Calc--rate the reverberation time for a hall of volume 1400 m3, which has seating capacity
110 percons with full capacity of audience and when audience are occupying only
cushioned seats. The relevant data for the hall are: tsI
SN Surface Area (nt') Coeffi cient of absomtion
I Plastered Wall 98 0.03
2 Plastered Ceiling 144 0.04
3 Wooden Door 15 0.06
4 Cushioned Chairs 88 1.00
5 Audience 150 4.70
4. Prove that the condition for achromatism for the combination of two lenses of focal
length fr and f2 having dispersive power !-vl and w2 plaoed at a separation x is tsI

***=*(w,+wr)
f, f2 f'fr' t "
Also prove that the separation between the lenses is equal to the focal length if 6 = 6.
5. In He-Ne laser, the lasing action is due to Ne gas. Then what is the role of the gas in it?
Explain how the He-Ne.laser works with a suitable energy level diagram on the basis of
four level scheme for its action. t5I
6. Two sotrces of intensities 4I and I are used in an interference experiment. Obtain the
intensities at points where the waves from two sources superimpose with a phase
rI
difference of (a) 0 (b) (c) n.
*,r^ tsI

Explain the dispersive and resolving power of a diffraction grating. Prove that the ratio of
dispersive power to resolving power is equal to the ratio of half width of peak and
 I

I
I

7. Derive the necessary formula for linearly, circularly and elliptically polarized light when t

light is emerged out of the doubly refraction crystal. tsl

t
8. What are Newron's rings? Derive tlie relation for the diameter of bright rings. What is the I
difference between the rings observed by reflected light and by transmitted light? Explain l

how does the pattern appear when white light is used? IsI
Define electric displacement vector. Develop a relation between electric displacement
vector, electric field and polarization. AIso prove that induced charge in dielectric is
always less than free charge. t5I
OR

A dielectric sphere of ra{ius R is charged uniformly. Obtain expressions for electic field
intensity (a) outside (b) dt\the surface and (c) inside the sphere.
I0. To similar balls each of mass m are hung from silk threads gf length I and carry similr
charges q. Assume that the angle made by each thread with vertical, 0 is small. Show that

*=(= *rr"r" is separation between the balls. AIso calculate the

ms)l',
charge q on
(2neo"t
the hung mass if I = 7.2 m, m: 20 g and x = 3 cm. t5]
I I. The parallel plates in a capacitor, with a plate area of 8.5 cm2 and air filled separation of
3 mm are charged by a 6 V battery. They are then disconnected from the baftery and
pulled apart to a separation of 8 mm. Neglecting fringing, find (a) the potential difference
between the plates (b) the initial energy stored and (c) final energy stored. t5I
'oR
, ,itA capacitor discharges through a resistor R. (a) After how many times constant (rr) does
- charge fall to one halfof its original value? O) After how many time constants does the
stored energy drop to half of ia initial value?

I What is Biot-Savart law? Derive an expression for flux density due to a current carrying
circular loop at its axial point. tsl
13.If a parallel plate capacitor with circular plate be charged, prove that the induced
magrretic field at a distance r in the region between the plates be t5l
ldE
n=iro.otfr fo1 rsR and

g= I po eo R2 99 fo, ,>R
22rdt
ru7lna Hall-effect experiment, a current of 3,{ sent lengthwise through a conductor I cm
V wide,4 cm long and I pm thick, produces a transverse Hall voltage of l0 pV, when a
magn:tic field of 1.5 T is passed perpendicularly through the thickness of the conductor.
Calculate (a) drift velocity of the charge carriers and (b) the number density of charge
carriers. t5I
.v]5. Define poynting vector and develop an expression of it interms of electic and magnetic
fields. Using the poynting vector calculate the maximum electric and magnetic fields for
sun-light if the solar constantis 1.4 KW#. ts]
16. A beam ofelectrons having energy ofeach 3 eV is incident on a potential barrier offinite
height 4 eV. If the width of the banier is 20 Ao, calculate the percentage transmission of
 03 TRIBHUVAN UNIVERSITY Exam. Re gular
TNSTITUTE OF ENGINEERING Level BE Full Marks 80
BCE, BGE,
Examination Control Division Programme Pass Marks 32
BME
2070 Bhadra Year / Part I / II Time 3 hrs.

Suhject: - Engineering Physics (5H452)

/ Candidates are required to give their ansrvers in their oum words as far as practicable.
/ Aaempt All questions.
{ llLquections caruy equal marks.
/ Assume suitable data if necessary.

l. Derive a relation to determine the radius of gyration of a compound pendulum. Why

deterrnination of the acceleration due to gravity is more accurate from a compound
pendulum than a simple pendulum?
OR
Define the quality factor (Q)- Derive a reiation of quality factor (Q) from the damped
harmonic motion and show that the quality factor (Q) is inversely proportional to
damping constant (b).
2. An oscillatory motion of a body is represented by y = uebt *here y is displacement in
time t, a is its amplitude and o is angular frequency. Show that the motion is simple
harmonic.
3. What is Ultrasound? How these waves are produced? Differentiate such waves from
ordinary sound rvave.
4. Why colours are observed when soap bubble is exposed to sunlight? Show that the
film increases
consecutive bright or dark fringes are observed when the thickness of the
.by -:L.in an inclined plane.
'2
OR
What is plane diftaction grating? How is it used to find the wavelenglh of a
monochromatic light experirneatally?
5. What is an optical fiber? How is it made? Write down the main differences between step
index and graded index multimode optical fibers with well diagrams.
6. A 200 mm long glass tube is filled with a solution of sugar, containing l5 grn of sugar in 4

100 ml of water. The plane of potarized ligh! passing through this solution, is rotated
ttuough 25"17'. Find the specific rotation of sugar.
I

7. Two thin converging lenses of focal lengths 0-2 m and 0.3 m are placed coaxially 0.1 m
apart in air. An object is located 0.6 m in front of the lens of smaller focal length. Find the .

position of principal points and that of image.

8. What is double refraction? Show thxa beam of plane polarized light is converted into
:

elliptically polarized light when it passes through a quarter-wave plate.

 9. Obtain an expression for electric field at an axial distance x from the centre of the flat
circular disc of radius R that ca:ries a uniform surface charge density o. Extend your
result to calculate potential at a distance x.
OR
A thin ring made of piastic of radius R is uniformly charged with linear charge density 1,.
Calculate the electric field intensity at any point at an axial distance Y from the centre. [f
electon is constrained to be in axial line of the same ring, show that the motion cf
electron is simple harmorric.
10. A copper strip 2.5 cm wide and 1.5 mm thick is placed in magnetic field with B:2.5 T
perpendicular to the plane of the srip and away from the reader. [f a current of 250 A is
set up in the strip, what Hall potential difference appears across the strip? Charge density
is copper: 8.4 x 1028/m3.
I l. Compare Ampere's law with Biot Savart law. Obtain expressions for magnetic field
intensity inside and outside the long straight wire carryiry current.
12. A spherical drop of u'ater carrying a charge of 30 pC has a potential of 500 V at its
surface (with V = 0 at infinity). (a) What is the radius of the drop? (b) If two such drops
of the same charge and radius combine to form a single spherical drop, what is the
potential at the surface of the new-drop?

13. Calculate the displacement current between the capacitor plut.s of area 1.5 x l0-2 rn2 and
rate of electric field change is 1.5 x l0l2 V/ms. Also fipd the value of displacement
current.
14. Obtain expressions for growth and decay of charges in the RC circuits. Explain how you
will measure experimentally the capacitance of the given capacitor.
$ Write down Maxwell equation in integral fonn with their physical meanings. Convert
. differential form.
these equations into

16. An electron is confined to an infinite height box of size 0- I nm. Calculate the ground state
energy of the electron. How this electron can be put to tk third energy level?
***

L-
 .?

03 TRIBHUVAN I.JNIVERSITY Exam. Ncrl lJack (2066 & Larcr Batch) I

INSTITUTE OF ENGINEERING Level BE Full Marks 80

BCE, BGE,
Examination Control Division Programme Pass Marks 32
BME
' 2074 Magh Yezr lParl I/II Time 3 hrs. .:ii

Subject: Physics (sH452) l

j

./ Candidates are required to give their answers in their own words as far as practicable.
.{

t Auempt&lquestions.
/ Att quesfio* carry equal marls.
{ Assume suitable data if necessary.

l. A uniform circular disc of radius R oscillates in a vertical plane about a horizontal axis.
Show that disc will oscillate with the minimum time period when the distance of the axis

of rotation from the center i, *

g
"lz
G*
-r- ? rtb oR
In..-1hp progressive wave show that the potential energy and kinetic energy of every
particle vEll change with tirne but the average energy per unit volume remains constant-

2. A 21$ Sapacitor is charged up to 50 Volt. The battery is disconnected and 50mH is

connected across the capacitor so that the LC oscillation occurs. Calculate the maximum
valudof the current in the circuit.
3. Shoy{that the least possible distance between an object and its real image in a convex
lens'tii four times the focal length of the lens.
t
4. What is path difference and phase difference in interference? Exptain why we have to
makerti'iompensation in path diff'erence in interference of light in pa.rallel fik+ in
reflected system. Hence find out the condition for obtaining maxima in interference in'
this film by reflected light.
'6roR
What is Nicol Prism? How is it constructed? Discuss some of it applications.
5. A diffraction grating used at normal distance gives a green line I:5400A" in-a certain
order superimposed on the violet line tr =4500Ao of the next higher order. If the angle of
diffraction is 10", how many lines are there per centimeter in the grating?
6- What are Resolving Power and dispersive power t-rf a diffraction grating? Show that the
resolving power of a grating depends on the order and no of rulirrgs of grating.
7. Calculate the reverbation time in a hall measuring 40*10*20t ft with the following
parameters. (i) 7500'sq.ft of plaster, ur:0.03 (ii) 400 sq.ft of glass, cr2:0.025
(iii) 6000sq.ft.of wood aqd floor etc, s,3:0.06 (iv) 600 seats cr+==0.03 and (v) audience of
500 persons, a5:4.0 person-
L V/hat do you mean by Numerical Apernrre and acceptance angle? Show that Numerical
Apeture fi'fA) is proportional to square root of fiactional refractive index change.

't 'l
 9. Derive an expression for the electric field intensity at any point in the axial Iine of a ring

of charge q. From your result show thar electric field is maximum at x = { , where a is
"12
the radius of the ring.
OR
A capacitor of capacitance C is charged through a resistor obtains an expression for
charging current. Show the variation of current with time. How will you use this
information to calculate capacitance C.
10. What will be the force per unit area with which plates of parallel plate capacitor attract
each other if they are separated by lmm and maintained at 100 V potential diflerence and
. electric constant of the medium in unity.

I l. Obtain Ohm's law in term of i = oB , Explain why and how resistance of a conductor
varies with temperature- Based on this information explain superconductor. Give at least
tu,o characteristics of superconductors.
I
12. Compare Arnpere's larv with Biot-Savart's law. Which is more useful for calculating B
I for a current carrying conductor. Calcuiate the magnetic field inside and outside a long
straight wire carrying current I.
OR
State Faraday's law of Electromagnetic induction. Show that in electromagnetic induction
the mechanical energy is converted into electric and finally in to heat energy.

13. A solenoid having an inductance of 6.3pH is connected in series with 1.2 KO resistor.
(i) If a l4V battery is connected across the pair, how long will it take for the current to
reach 8Ao/o of its equilibriurrr valu€? (ii) What is the current through the resistor at time
t:rl
14. What is Hall effect? Obtain an expression fcr Hall resistance. Shou,in a graph how hall
resisiance varies with magnetic field.

15. Calculate the magnitude of the poyniting vector and the amplitude of the electrie and
magnetic fields at a distance of ! 0 cm from a radio station v,,hich is radiating power of 105
watt uniformly over a hemisphere with radio station as center.
16. Consider an electron of mass rn is confined in an one dimensional infinite potential weii
of width / such that
V=ofor0sxandx2l
V:0far0<x<l
show that inside the well electron can only harre the discrete energy values.

'd'
.,'5'
 !

03 TRIBHWA}.IT'NTVERSITY, Er*m. llcgular (2066 ,,t Lrrfcr Bltch)

i- INSTITUTE OF ENGINEERING Level BE FultMarla 80
Examination Control Division' Programme BCE,BME Pass llflarlcs 32
2069 Bhadra Year / Part r/il Time 3 hrs.

t-

I / Candidates are required to give their answers in their own words as far as practicable.
{ AnemptAll questions.
{ All questions carry equal marks.
I
{ Assune suitable data if rucessary-
lE

1. What are drawbacks of simple pendulum? Show tbat the period of torsion oscillations
I remain unaffected even if the amplitude be large, provided that the elastic limit of the
L suspension wire is not exceeded.

i
OR
I

! In simple harmonic motion, when the displacement is one-half the amplitude, what
fraction of the total energy is kinetic energy and what fraction is potential energy? At
what displacement is half kinetio energy and half potential energy?
L 2. Derive a differential equation of LC oscillation. With the solution of this equation, show
t$t the ma:<imum value'of electric and magnetic energies stored in LC circuits is equal.
3. How much acoustic power e.nters the window of area 1.58m2, through the sound wave
t- (standard intensity level l0-'\M/cmt9 The window opeilr on a street where the street
noise results in an intensity level at the window of 60d8.
I

\- 4. Explain circle of least confusion. Show that the diameter of a circle of least confusion is
independent ofthe focal length ofa lens.
5. A gtass clad fibre is made with core glass of refractive index 1.5 and cladding is doped to

\- grvs a fractional index difference of 0.005. Find (i) the cladding index (ii) The critical
inte*a reflection angte (iii)' The external critical acceptance angle (iv) Numerical
aperture (v) Acceptance angle.

6. A parallel beam of light(1,=5890A) is incident on a thin glass plate ( p = 1.5) such that the
angle of refraction is 60o. Cal'culate the smallest thickness of the plate which will appear
Aot Uy reflection.
7. . How are Newto4's Rings formed? How is the ring diameter and film thickness related?
How can Newton's rings experiment be used to determine refractive index of a liquid?
OR
What is double refraction? How can que experimentally distinguish between plane
polarized, circularly polarized and elliptically polarized light?
8. Assume that the limits of the visible spectum are arbitrary chosen as 430nrn and 680nm.
Calculate the no. of rulings per millimeter of a gating that will spread the first-order
spectrum through an angle of 2A'
9. Define an electric dipole. How does a dipole behave in electric freld? Obtain the
oonditions for maximum torque and-yaximtrm poterftial energy in an electric field.
OR

i-
I

For the charge configuration of the figure, show that VG) al a point P on the line

assumin! a is given by v = I

:>> #(:.?)
#
,r
a E a ,s P
-q +Q +q
i.
10.A long cylindrical conductor has length lm and is surrounded by a co-a:dal eylindrical
conducting shell with inner radius double that of Iong cylindrical conductor. Calculate the
. capacitance for this capacitor assuming that there is vacuum in space betrveen cylinders.
1 uniform volume density 3.2pClms fill a non conducting solid sphere of radius
1. Charges of
5cm. What is the magnitude of the electic field at (a) 3.5cm (b) 8cm from the cente of
the sphere?
12. What are superconductors? How ttrey differ from perfect conductors? Give basic
properties and uses of superconductors.
13. Derive the relation for rise and fall of current in LR circuit. Plot a graph betneen current
and time and explain the graph. ,
OR
In a Hall-effect experiment a current of 34' sent length wise through a cpnductor I cm
wide, 4cm long and l0frn thick produces a tansverse (across the width) Hall potential
differences of l0pV, when a magnetic field of 1.5T is passes perpendicularly through the
thickness of conductor. From ttrese dat4 frnd: (a) The drift velocity of the charge carrier
and O) The number density of chargc carrier.

14. A particular cyclotron is designed with dees of radius R : 75bm and with magnets that
can provide a field of 1.5T. (i) To what frequency should be oscillator be set if deuterons
arq to be accelerated? (ii) What is the ma:<imum energy of deuGrons that can be
obtained? Given mass of the deuteron is 3.34x10-27kg.

15. Define Poynting vector. Prove that 3 = -' '- -'

;l.""J
16. Prove that the energy levels are quantized, when the electon is confined in an infinite
potential well of width a.
***
 03 TRIBHWANI,JNIVERSITY Exam. Regular
INSTITUTE OF ENGINEERING Leyel BE FuIlMarks 80
Examination Control Division Programme BCE,BME Pass Marks 32
2068 BhadrL Year / Part I/II Time 3 hrs.

Subiect: Physics
/ Candidates are required to give their answbrs in their own words as far as practicable.
/ Anempt All questigns.
/ .a.U questions carry equal marlu.
/ Assume suitable data if necessary.

1. What is forced oscillation? Derive differential equation for forced oscillation and show
that amplitude at resonance is inversely proportional to damping constant of medium.

OR
Derive the differential equation for damped LCR osciliation. Obtain an expression for
current and frequency of oscillation.
2. Prove that if a hansverse wave is traveling along a stuetched string, the slope at any point
of the string is numerically equal to the ratio of the particle speed to the wave speed at
that point.
3. The volume of a room is 600m3, wall area of room is 22M, the floor and ceiling area
each is l2Om2.If average absorption coefficient for walls is 0.03, for ceiling is 0,80 and
for floor is 0.06,. calgulate average absorption coefficient and reverberation time.
4. Two thin lenses of power Pr and Pz are separated by a distance d. Find an expression to
show that equivalent power of the combination is given as P : Pr * Pz - dPrPz.
5. Explain the formation ofNewton's ring in reflected light. Prove that, in reflected light the
diameter of the dark rings are proportional to the square root of natural nirmbers and
diameter of bright rings are proportional to the square root of odd numbers.
OR
Write dovm the physical meanings of dispersive power and resolving power of plane
transmission gratting. Show that both resolving and dispersive power have proportional
relation with the order of spectrum.
6. A 2OOmm long tube containing 48cm3 of sugar solution produces an optical rotation of
11o whenplaced in apolarimeter. If specific iotation of sugar solution is 66o, calculate
quantity of sugar contained in the form of solution.
7. Light is incident normally on a gratting 0.5cm wide with 2500 lines. Find the angles of
diffraction for the principal macima of the two sodium lines in the first order spectnrm,
Ir : 5890A' and ?u2 :58964'o. Are the two lines resolved?
8. What is principle of laser? Discuss how population inversion is carried out? With the help
of energy level diagram, explainhow He-Ne laser works. '
g. A thin non conducting rod of finite length I ca:ries a total charge q spread unifolmly
along it. Show that the electric field at any point at a distance y above from the centre of
rod is E: -+- ,
1
Extend this result:for infinite length. '.:.
4xery .ltz + +y2
,.

OR
Find the potential at any point at an angle 0 at a distance r from the centre of the short
dipole. What result do you obtain if the point is along a,xial line?
10. A capacitor is made of two concentric spherical plates of radii a and b of inner and outer
spheres respectively. Ifouter plate is positively charged and inner sphere is earthed, prove

that the capacitance of such capacitor is given as, C: *eo[*]

11. Calculate the relaxation time for the electrons of sodium atom. The number of atoms per
cm3 in sodium is 2.5x1022 , and the electrical conductivity is 1 .9 x 107 s/m.

12. Listand explain methods to calculate magnetic field due to a current ca:rying conductor.
Derive an expression for the magnetic field on the a:cial line of a long solenoid carrying
current.
OR
What is self inductance? Calculate the inductance of a circular.Toroid. From your result,
show that inductance is a property of a coil and depends on permeability and shape and
size of the coil.
13. Suppose a cyclotion is operated at an oscillator frequency of 12MHz and has a dee of
radius 53cm.
a) What is the magnitude of the magnetic field needed for deuteron to be accelerated in
the cyclotron?
b) What is the resulting kinetic energy of the deuteron? Given: mass of
deuteron : 3.3 4xl0-27 kg.
14. What must be the magnitude of a uniform eleckic field if it is to have the same energy
density that passed by a 0.50T magnetic field?
15. What is poynting vector? Show that the intensity of an electromagnetic wave equals. the
average magnetic energy densitytimes the speed of light.
16. A particle is moving in one dimensional potential well of infinite height and width a. find
the expression for energy of the particle.

;. i_. ,...:,
 'p3 TRTBHWAN UNIVERSITY Exam. Regular / Back
INSTITUIE OF ENGINEERING Level BE Full Marks 80

Examination Control Division Programme BCE,BME Pass Marks 32

2067 Mangsir Year / Part Utl Time 3 hrs.

'/ Candidates are required to give their answers in their own words as far as practicable.
/ Attempt All questions.
/ All -questions carry equal marlcs.
/ Assume suitable data if necessary.

1. What is a torsional pendulum? Obtain an expression for its time period and explain why,
unlike a simple or a compound pendulum the time period in this case remains unaffected
even if the amplitude be large?
OR
Derive the differential equation of the forced oscillation of LCR circuit with ac source
and find the expression for the cu:ent amplitude.
2. A meter stick suspended from one end swings as a physical pendulum (a) what is the
period of oscillation (b) what would be the length of the simple pendulum that would
have the same period
3. Calculate the minimum intensity of audiability in watts per square cm from a note of
1000 Hz if the amplittrde of vibration is 10icm. Given density of air is 0.0013 gm/cc and
velocity of sound in air is 340 m/s.
4. What is diffraction of light? Discuss the intensity distribution with special reference to
diffraction of light in a single slit.
OR

Define circle of least confusion and show that d = 1WO.

2
Where
d = diameter of circle of least confusion
W = disp-ersive power
D - diameter of lens aperture
5. A plano-convex lens of radius 300cm is placed on an optically flat glass plate and is
illuminated by monochromatic light. The diameter of the 8e dark ring in the transmitted
system is 0.72cm. Calculate the wavelength of light used.
6. What is double refraction? Using the concept of double refraction show that the plane
polarized and circularlypolarized light are the special cases of ellipticallypolarized light.
'1. Two similar thin convex lenses of focal length 10cm each are placed co-axially 5cm
apart. Find the equivalent focal length and the position of principal points. Also find the
pgsition of the object for which the image is formed at infinity.
S. What is an optical fibre? Discuss its qpes. Derive the relation for Numerical Aperture
(NA) in an optical fibre.
9. Find the electric field at a distance x above the centre of the flat circular disc of radius R )
which carries a uniform surface charge density o. Extend your result in the limit R -+ o.
OR
Show that the electric field due to a short dipole at a point on the axial line is turice as that
of a point on the equaterial line.
10. Differentiate between polar and non-polar dielectrics. Using Gauss's law in dielectrics
establish relation of electric field with displacement vector and polarization vector. Hence
obtain the relation for free and induced charge in the dielectric.
ll. What is the average time between collisions of free eleckons in a copper wire?
(At. wt. : 63 glmol, density : 9 gmlcc and resistivity = 1.7 x 104 C)rn,
NA:6.02 x 1023 mo r)
12. A spherical drop of water carrying a charge of 3 pC has a potential of 500V at its surface.
What is the radius of drop? If two such drops of same charge and radius are combined,
what is potential of the single new drop formed?
13. A variable field of1012 Vlm.s is applied to a parallel plate capacitor with circular plates
of diameter 10cm. Calculate (a) induced magnetic field and (b) displacement cunent.
14. A circular coil having radius R carries a current I. Calculate the magnetic flux density at
an axial distance x from the centre of the coil. Explain how the coil behaves for a large
distance poi4t and at what condition field will be ma:<imum?
OR
Show that the energy per unit volume in electic field and magnetic field are proportional
to the square ofJtreir fields.
15. Derive the Schrodinger time independent wave equation. What is the physical
significance of wave functions?
-+
16. Using Ma:cwell equations in free space, derive electromagnetic wave equations for E and
B. Write its plane wave solution.
,F**
 .l
OI TRIBHIJVAN UNIVERSITY Exam. New Back Batch
INSTITUTE OF ENGTNEERING Level BE Frrll Marks 80
Examination Corrirol Division Programme BCE, BI.1E ll:isg I\1[arks
2O67 Chaitra Year / Part Ufi -- I lnle j"ffi-.

&tbiect: Physics
'/ Candidates are required to give their answers in their own words as far as practicable.
/ Attempt All questions.
/ eU questions carry equal marlcs.
/ Assilme suitable data if necessaty.

l. Derive a relation for the time period of a compound pendulum and compare it with that of
simple pendulum to locate the centre of oscillation.
n
OR
Obtain differential equation for forced oscillation. Write .its solution. Explain the
statement "quality factor (Q) is a measure of the sharpness of resonance in the case of a
driven oscillator".
2. Derive a relation.for speed of a stretched string and show that the
avera.ge rate of energy'transfer is Wher.e the'symbols are having usual
meanines.
-:i... I .r"i.. ,de? Yrf
3. Write down the requuements for a good acoustic hall and derive a relation for
reverberation time. i
4. Explain chromatic aberration. Show that the longitudinal chromatic aberratidn is equal to i
the product of dispersive. I-lD-.r er and meari focai iength of a lers.
OR
Def,rne the term "optical activity''. Derive d relation for the specific retation of any
optically active substance. Also write down its applications.
5. A glass clad fiber is made,$ittr tte core glass of refractive index 1.5 and the cladding is

_doped to give a fractional index change of 0.0005. Determine

a) the cladding index, .'
b).the acceptance angle and
. c) therrumerical aperture. I '' ,'' ' :.'';'-. '.

6. Nervton's rings are observed in reflected light of wavelength 5900A. The diameter of 1Oth

dark ring is 50mm. Find the radius of curvature of lens and thickness of air frlm.
7. In a grating the sodium doublet (5890A, 58964) is viewed in third order at -10" to the
normal and i5 resolved. Determine the grating element and.the total.width cf thg luiings.
L Calculate the thickness of (i) a quar,:er wave plaie and (ii) a half wave plate given that
pg = 1.553, ',4: l-544 and l' : 5x10-5cm.
g. What is electric Quadrapole? Finding an expression for electric potential at any point on
an axial line at a distance 'r' from centre of short Quadrapole, show that electric field at
that point is inversely proportional to rl. g-- _ ez q-Un,
A ringof radius'R' is carrying a unilonliydistributed charge'q'. Find an expressiotr for
electric field at any point on the axial line. Locate the point at whicl'r electric field is
 ln. A parallei plate capacitor each of area l00cnl2 hr's a p'd of 50'V and capacitance of
ICOxlC-" f.f. ff a mica of di,:lecLric col:sla;lt r.. ,: .:ls'.t. j t':'rv':':r pia'cs iinti lhe
magnitude

t
of
Electric fietd in mica
b) Displacement vector
'1),/
v
c) Potarizationvector ,
11. Compare the methods of Biot Savart law and Ampere's law to calculate rnagnetic fields
ciue to surient canryine conductor. Calculate m:gnetic field at an axial distance from 'r'
the centre of the circular coil carrying current.

12.A current of 1.2x10-loA exists in a copper wire (At. wt.:63 and density = 9gm/cc)
rvhose diameter is 2.5mm- Assuming current to be uniform, calculate:
a) Current density
b) Electrical conductivity
c) Mobility of electrons
: -
13.What is cyclotron? Find an expression to show that maxinrum kinetic energy of charge
particles coming out of dees of cyclotron is directly proportional to square of freQuency of
oscillator
OR
What is.'Hall'-effect? Derive an expression for Hall eoefficient'and'establisli the relation.
' ' ; ' r'''.
:
with mobiiiiy orcharge lariiei aiiiA';l#iauctivity of materia! of wire. ' .
!4. A rrct...,n with, sneed of 3x10s m/s orbits just outside a charged sphere of radius lcm.
\Vhat is the charge on the sphere?
l5.Write Maxrvell equations in integral form. Corrvert them in differential fonn. Expiarn
each equations.

i6. A free particle is confined in a box of width L. find an expression for energy eigen value
to sirow that the particle can have only discrete energy and momentum. :
'.{, **{:

!+
 O6 TII.IBI.!UVA'\ T,,NIVERSITY
P-r.llr, Old Back & E,arlier R
INSTITUTE OF ENGINEERING Level BE Full Marks , 80 I

Examinqtion Control Division Prograrnme BCE, B.Agri. Pass Marks 32- t-l
,

2067 Chaitra Year / Part

-I/II Time 3E;.-'
.:

:.

'/ Candidates are required to give their answers in their own words as far as practicable.
i Artempt any Six questions ietecting One each from Group A & D and Tio each front
Group B & C-
'/ Thefigures in the margin indicate FulI Marks.
/ Assume suitable data if necessary.

Group A
l. a) Define physical pendulum. Show that the radius of gyration is eQual to distance from
centre of suspension to centre of gravity of a compound pendulum, when time period
is minimuni. ll+sl
I
b) A solid sp.here of mass 5l2kg and diameter 217 m is suspended on'a thin metallic
. wire. Find the period of angular oscillation if the torque gonslqnt of the wiie is
t.

c) What are particle.velocity and wavevelocity? Find the relation between them. t3l
2. a) Differentiate between reverberation and echo. Derive a relation for the reverberation
time with reference to acousticatly fit hall.
b) A rnass cf 5 kg stretches a sprirrg 0.3rn fionr its equilibrium prl5i1ien. Tne mass is
I
removed and another body of mass 1.0 kg is hanged from the spring. What would be
tlre period of oscillation if the spring is now stretched and released? t3l
c) The relaxation time for a damped harmonic oscillator is 50 seconds. Determine the
time in which the amplitude and energy of oscillator falls to l/e times of its initial
value. t4l

3. a) What are coherent sources of light? Why it is essential to generate coherent sources to
observe the interference? Show that there is.zero energy at dark fringes of interference
phenomena. tl+l+31 Il
b) Differentiate between curvature of field and distortion. Also draw neat and clean
diagram of such aberrations. t2.5+2-5) i
c) In a plane transmission grating the angle of diffraction for second order maxima for
wavelength 5 x l0-s cm is 30". Calculate the number of lines in one cm of the grating
surface. t4l
4. a) Explain the phenomenon of double refraction in uniaxial crystal. What are quarter
wave and half wave plates? t6l
-- b) Discuss the propagation mechanisms of light waves in optical fiber. t4l
c) Distance between two slits is 0. lnrnr and the width of the fringes fonned on the screetr
is 5mm. If the distance between the screen and the slit is one nleter, what would be
the u'avelength of light used? t4l
 5. a) Discuss the essential requirenrents for producing laser action. Describe a Ne-Ne laser. t5l
b) Two thin convex lenses having 6cal lengths 6cm and Zcm areco-axial and separated
by a distance- of 4cm. Calculate the combined focal length and the positions of the
piincipal Planes- tsl i

c) A 20cm long tube containing sugar solution rotates the plane of polarization by I1". If
: the specific rotation of sugar is 66", calculate the strength of the solution. t4l
I

Group C
6. a) Define dielectric strength. Derive a relation for the capacitance of a spherical
.- capacitor consisting of two concentric spherical shell of radii y and z, (with z> y). lt+sl
b) If a copper wire is stretched to make it 2.5o/o longer than its original length, what is
- the percentage change in resistance? .
l4l
b) List industrial uses and hazard of high intensity electrostatic field. Explain in detail,
one ofthe uses. t3l
7. a) Explain resistivity. Obtain the expression for resistivity in terms of mean free path. tsl
; b)' Stite Biot-Savarts-.law. Usp it to determine themagnetic field of a narrow circular coil
along its axis. tll
. r- J

c) The current in a LR circuit builds up. to one third of its steady state value in 5 sec.
What is the inductive time constant? :

,, t3l
J

8. a) State the Arnpere's circuital law. Derive the relation for the self induction of a toroid. - tsl
f--ir). 'f;'v.) particlcs'cf equzi-cliarSes +f 2.0 :r.-l.O.k' hrit.oppq.Fjle-stgn-s ar-E [el4--1-ic.rf _ap-a-rt-._._ .* *.*-
.i+
rvhat are the magnitudes and direclions of E at a point midway between them? t4I
c) A copper strip 2cm wide and lmm tlricl< is placed in a magnetic field rvith B : 1.5T.
Ifa current of 200,4' is setup in the strip, rvhat Hall p.d. dppears across the strip?
(Given: n : 8.4 x 1028 per m31 l4l
I
.:.' .
D.,
."1
I
I GrouD ':, '

9. a) What is displacem'ent current? Also write its iignificance. t3l

_l

I
b) Derive a diffirential equation- for LC opcillation rvith initial charge Qe. Derive an
expression for the frequency of the oscilLition, then relate it with spring-mass system. t6]
!

c) A 10 Henry coil has a resistance of 180Q What size of capacitor must be put in series
with it if the cornbination is to resonarit u,hen connected to 60 Hz outlet? t4l

10. a) With tlre help of Maxwell's equations prove the relation C = -_ I , where symbols
ri €o Fo
carry their usual meanings. t4l

b) Prove the continuity relation i.i* $ = o. t4l

a
c) The maximum electric field at a distance of 20m from an isotropic point light source
is 4.0 v/m. Calculate (i) the maximum value of the magnetic field and (ii) the average
intensity of lighr there. t5l
 I
,r- I 06 TzuBHUVAi.i t intVEnStrY
. INSTITUTE OF ENGINEERING Level BE Full Marks 80

Examination Control Division Programme BCE, B.Agi. Pass Marks 32

2066 Magh Year / Part I/II Time 3 hrs-

J CandidaJes are required to give their answers in their own words as far as practic4ble.
./ Attempt anlt Six questions selecting One eacfrfrom Grouo A & D and Two eachfrom
Group B & C.
./ Thefi.gures in the margin indicate Fttlt Marks.
./ Assume suitable data if necessary.

Group A
1: a) What is torsional pendrrlum? Shou' that motion of a disc of a torsional pendulum is
harrnonic. Find its time period. Describe horv u,ill you determine modulus of rigiciity
of a thin metallic wire which supports the disc- U)
b) The amplitude of a lightly- damped oscillator decreases by 3% during bach cyc1e.
What fraction of the energy of the oscillator is lost in each full oscillation? _ [3]
c) A source of sountl has a frequency 2.56 Hz and amplitude of Q.25cm. Calcuiate the
flow of energy across a squaxe centimeter in one second if.the veiocity'of second in.
air is 340 m/s and the density of air is 0.00129 gn/cc. t3l
2.., a) ,i[hat is reverberation? d"Eyg. the rgverberation time and explain how it dejends oir
aUsorption coefficient oittr'A"dium. DiscuS$''-ft significance of tliis fon[Uia,.'with.' ] 'r :" ;i' ;','.''7:';''
reference to the. acoustics of a building. . t7l
b) Derive an expression for velocity of a wave in a stretched sfi5rg. t3]
c) Two sounds differ iri iound levei by 1.00 dB. What is the ratio of the greater inlensity.
to the smaller intensity? t3]
Grouo B
3. a) What is an optical fiber? Expiain the physics behind its firnctioning. Trace the ray .

diagram that shows the propagation of light through the step index and graded index
optical fibres. i7l
b) Define cardinal points and iocate these points within the lens. . .
I3l
c) A dielectric siab of thickness 'b' is inserted between the plates of a parallel-plate '

capacitor of plate separation .ld'. Show that the capacitance is then given by
u=
Ke, A where the slmbois have their usual meanings.
--_-{i^, t4l
Kd-b(K-1)'
4. a)-Explain the phenomenon of interfbredce of light. Give the theory of the Newtcn's
'/ ring. Hor,v fringes can be used to fi.nd the wavelength of iigirt. t6l
b) Light is incident normally on a gratting of total ruled rvidth 5x10'3m with 2500 lines
in a cell. Find the angular separarion of the sodium lines in the first order spectrum.
\Var,elengths of iines are 589nm and 589.6nm. Can they be seen distinctly? t4l
c) \\,hat is astigmatism? What ls the cause of it and how can it be reduced to a
minimum? L"+ l
5. 3) Write dor.vn the physical meanings of dispersive power and resolving power of plane
r- 1

proportiona1reiationwiththeorderofthespectrum. L/.i

t CUarter.rvave oiate 1s 12.5 pinf thick. Calcu.lale ihe wavei.retn ftir w'irich ri acts as a -
_i) ,quaner wave piate- 'ine difi'erence i:-: :.le pri:rclpal refractive inorces rs J.C i.

{ fioa the specific rotation of a given sample of sugar soluiion if the plane of
poiarizatiol js turned through 26.4". The length of the tube containtng 2Ao/o sugar
soiuiil:r i,s lilc:n.
 Group C
6 a) A thin ring made of plastic of radius R is uniformly charged with linear charge
density 1". Calcuiate the electric field at any point at an axial distance Y from the
center. If electron is constrained to be in axial line of the same ring, show that motion
of electron is simple harmonic- Find frequency of osciilation. Mention any
assumptions you made. t,r
b) In the given figure, frnd the currents ir, iz, i; if.Er E2 : 3V, Rr : R1 = 2Q and
=1.5V,
&=4Q' L-l
Ez

4-
,
L
I
R1
ll i"l
v
I la
i,
-l

-c) A copper strip 2cm wide and 1mm thick is placed in a magnetic {ield with B: 1.5 T
perpendiciilar to the plane of the stip and au'ay frorn the reacier..If a current of 2004
L rct up in the strip, what Hall potential difference appeairs across the strip? Charge
i
density of copper: 8.4 x 1028/m3; [3i
.l
7a) Define electric dipole. Find an expression for electric potentiai at any point in sPace
I

dueto-dipole"of length Za,.Could.you extend this relaticrt.to calculate electrii'fibld' '. ''

intensity?ilf'so, horv?
I
I
t5]
'b)
I

Wliat is the drift velociry of a copper lvire having diameter 0.25cm chrrying current of
., 10A? Given density of copper = 9 grn/cm3; dnd molar mass of the copper is
64 gmimole. t+j
;1
'c) What is the magnetic energy density at the centre of the circulating electron in the
h;vdrogen atom? Assume that the elecuon circulates around the nucleus in a path of
raciius 5.lxiO-llrn at a frequency.of 5.8xi0t5 revlsec. i'j
8.' a) Differentiate. -hetr';een Biot-savart iarv anc Ampere's law in caiculating magnetic fieid.
of a current carr;",ing conductor. Caiculate the ma-enetic field on..the axial line of a
._
,,:_ .

lo4g straigi:t solei:.oid'car4iing cuiieiii. ;':

" ''b) A capacitor of capac,ilg4ree,C is charged through the resistop|, Calculatetie time at
' r.vhich tJre potential acrcss ihe resistor is eqiial to the potential acrbss the capacitor. i-t i

c) Calculatethe capacitance of the earth, viewed as a spherical conductor of radius 6400km. I--il
i" I -

g. a) $ihr..t- is eiectromaEnetic -
oscillaton? Derive a riifferential equaticn for free em
cscillation. Finci the tirne period <;-l csciiiation. i'ior.v freq,.isr.:l -wiil be change,j if
ti::,.::e iS resistante in the circnir,' iii

b) Vi-r:;,'and.ho,,v fu[a:r-,reIl rnod.ifieC A.,::teiels laii i:l l;ag.netisui? !-,.

c.; CaicLdare tile iragrritud.i of eiectrir and i:a-Eneric fieici verctcrs asscciaied with e-n,
SCufCr-': -i:, lC-;..twa;,, ii,:S pov,a.:i Cf cifiS:i.ti lS 3il ii*.
\r-;:itr'es:,::i:iCi i':.'r-,:it a I

i: 1i'jle lv{ax-'veii':; e,tr-raticl ili ir-.'regr:,,i f,-:n:: a1d iiie ja-oi's in r.vi:ir::r r}e:ie er:r'i:a:ii.ns afe
/Y b;rse+. Col,,,ec
them into tLiiferential foii:r. L'-tj
EI
gtJ' Dertve eiectiomagnetic r,vave equaticns in fi"e space. Give their piane ..vave solution.

Based on these
.F,
solutions prove that 3 = C. t4j

ul - -.-.- -:- i>--v. v'eu--,-..^-;-i,*ru;.,.^ vrrer.>v, vzr.pruissCLr iii LCfltS Oiii-,g ma.Xim'am -

-a cirage, ls present on
_tlie capacitor vrhen the energy is shared equaliy between the
electric and magnetic fietd? t3J:
- :f *+
\
06 TRIBHWANI.INIVEPSTTT Exem. Regular/Back
INSTITUTE OF ENGINEERING LeveI BE F,ill l\{arks
Examination Control Division Programme BCE, Bigri. Pass ivlarks 32
2065 Chaitra Year / Part ufr Tirue 3 hrs-

Subject: - Physics
/ Candidates are required to give theA answers in their own words as far as practicablc.
': {" Atternpt any S* quations selectingat least Oneifrom Grouo A & D and fu1from Group B & C-
/ Thefigures in the margin indicate FuIl Marks.
/ Assume suitable data dnicessary.

Grouo A
1. a) What is a compound pendulum? Deduce the expression for the time period of a compound
pendulum and formulate the equivalent length of the simple pendulum. U+61
b) Calculate the change in intensity level when the intensity of sound increases 100 times the
. original intensity. t3l
c) A line sorrce e, its a cylindrical expurding wave. Assr:ming the medium absorbs no en€rry,
- find how the arylinrde and intensity of the wave deperrd on the .disence from the source. t3]
iiiirj::...'.' ':
. .-2,.,.. 4) Ffpl"i" S" trrp '3avp'rnoSoa'lr.Sh'rw that fur a p!4e pmg,',;ssive wa're, or th: averagq half
-' ' ."'r. :.-r, ':''
t.

theenergf iskiiraicadhalf.itotentiaL ,,i ,, . .,, .. ' ,-' .

,, . , [1-t5] ': - 'r r\fi:, .i!?i
b) A licture hall with a volume of 4500m3 is for:nd to have a reverberation time of
1,5 sec. What is tre totd absorbing power of all the surfaces in the hall? If the area of the
soud absorbing'srrface is 1600m2, calculate the avemge absorptim cobfficient t3]
c1 A sUng 2.7hm,lotghai a mass of 263 gm Thc tension in the sting is 36.1N. What :rmst be
tre frequency of tavelling waves of arrylitude 7.7mm in order that tlie a:verage transmitted
powerbe 85.5W? t4l

3. a) What are cardinal points of ,o *d"ffi, Determine the equivalent focal length of a
combinaticin of two thin lenses separated by a finite distance. Hence find the position of two
principalpoints . [1+5+2]

P)
Wf,at is an optic4J.fibd.rll.:"y.it it rnade?. Write down the main,difrerencel bejwcg.n
$ef
i3l
c) Calculate the thicloess of (i) a quarter wave plat'e and (ii) a half wave plate, liven that t31
ps : 1.553, 11a= L..544andi, = 5890A
4. a) What are monochromatic aberrations? Explain the term spherical aberration and astigmatism
and theirminimizatiotr n i+ suitable raydiagrams [1+7]
b) Newon's rings are formed by reflected light of wavelength 5895A with a liquid between the
plane and curved sr:rfaces. If the diameter of the 6e bright ring is 3mm and the radius of
curvedsurface is l0OcsL calculate therefractive indexofthe liquitl 14l
c) Distingrristr between Framhoffer and Fresnal diffraction. tzl
5- a) What is population inversion? Explain why laser action cafiist occur without population
inversion between alomic levels? ll+41
b) Explain circle of least confirsion. Show that diameter of circle of least confusiou is de'pendent
of the focal length of a lens. t5l
c) Two thin lenses of focal lengths fr antl fz separated by a distairce d have an equivalent focal
length 50cna The combination satisfies the conditions for no chromatic aberration and
minimum spherical aberration. Assuming both the lenses are made of same material, find the
values off1, f2 and d. t4l
 . Group C
6. a) State general form of Gauss larr. Calculate potential difference between two piates of a
charged cylindrical capacitor. isl
b) In the given circuit diagram, find the current in each resistor and potential difference between :

X and Y. t4I

6V

50c)

4Y
x

100c)
/
-+
c) A strip ofcopper l5Oprn wide is placed in a uniform rnagretic figfd B of nqgniru{e 0.65Tr i,i ,,. :

-+
with B perpendicular to ship. A current 23A is then sent tbrough the strip such that a Hall
potential difference V appears across the width of the ship. Calculate V. Given number of
charge carriers per volume for copper is 8.47x1028 electron/ml. t4l
7. a) What is dipole? Derive an expression for electic field due to dipole at the points on the (i)
axis of the dipole and (ii) perpendicular bisector of dipole. [1+3+.]l
b) Show that the time constant in RC circuit is the time at which the charge in the circuit will
I
reach avalue a of its final equilibrium value. t3]
e

c) Two long parallel wires are 8.lcrn. a.parL What amount of equal and antiparallel current flow
in the wires ifthe mapetic field haffiray between them is 296 W t3I
, _ ,9, a)-, Sta.p g1d e:rplain Faraday laws ritinduction. Deduce the expression_for the inductance of a

b) State Biot-Savart lew. Use it to ftiQ mapetic field at any point due to long skaight current
carniing conductor. [1+3]
c) What will be the force per unit area with which plates of parallel plate capacitor attract each
odrer if they are separated by lmm and maintained at 100V potential difference and electric
constant of the medium is unity. t4l
GroupD
9. a) Explain what are Maxwell's equations. Write Maxwell's equations in free sface and find the
electomagnetic equations for electric 2ad pagnetic field. Also provide their plane wave
solutions. rn
b) What is displacement current? Why Maxwell's modification is necessary is Ampere's law in
magnetism? t3l
c) You are grven an inductor of I rrll. If you are asked to make it oscillate with a frequeney of I
MIz, how can you make such an oscillating device? t3I
10. a) What are free and damped electomapetic oscillations? Deduce the frequency of a damped
etectromagnetic oscillation and hence show the charge disributiorvith time graphically.
_ IT
b) The maximum electric field at a distance lOm from an isotropic point light source is 2Vlm. (i)
Wtat is the average intensity of light there (ii) What is the power of the source? t4l

c) Show that the displacement current in a parallel plate capacitor is given t a

*.
Lzj
***
 .. .. :,:_-.j1.1,,

06 TRIBHWANUNTVERSITY Exam. Back

INSTITTJIE OF ENGINEERING Level BE FuIl Marks 80
Examination Control Division Programme BCE, B.Agri. Pass Marks 32
2065 Kartik I ITI
Year / Part Tlme 3 hrs.
,
Subiect: - Physics
/ Candidates are required to give their enswers in their own words as far as practicable.
{ A!t"*pt any Six questions selecing at least One from Gr?uo A and D and Two from
Grouo B and C.
/ All questions carry equal marla.
{ Thefigures in the margin indicate Full Marks.
/ Assume flitable data if necessary.

. . Grourr A
1. a) Differentiate between free oscillation aud forced oscillation t3l
:, .,-.-., ,..._:.," -i:....- .. t-.., -. .,. -,.j... .. -,-...1,
,i;rr;,i r, r :;1r."''',':..,'b) "Itlhat is torsitiniipindtrlum? Fina'ttre time period for torsion pelrduhrm,. fiso wdtC its, ' i11. l. | , r ;-r, .:

significauce. tsl
c) A spring is hung v_erti1atl..V and l.oafed d9. mass of 75 grams and allowed to
I
': , oscillate, calculate (i) the time period and (ii) the frequency of oscillation, when the
tsl
2. a) What are the differences betureen interference and beats? l3l
b) Define absorption coefficient? Derive Sabine's reverberation formula and also explain
its importance in our daily life? t6l
c) A police'man on duty detects a drop of 12 percent in the pirch of a motor car as it
crosses him. If the velocity of sormd is 332 m/s, calculate the speed of the car. l4l
Group B
Calculate the equivalent focal length of two thin.co-arial lenses sepaitted by a finite
distance x. Also derive expressions grvfulg the positions ofthe two principal points. 14+27
b) Write down the properties of LASER. Also explain the terms optical pumping,
population inversion and stimulated ernission. Write the merit and demerit of laser. U+3+1]

-c) In Newton's rings experiment the radius of the 4th and 12th rings are 0.26cm and
0.37cm respectivily. Find the diameter of the 24s dark ring. t3l
4. a) Wtat are the conditions for coherent sources? Explain the phenomenon of
interfer€,nce in thin filn for reflected liglrt. [l+5]
b) What is optical fibre? Explain the graded index multimode optical fibre and also write
the application of optical fibre in communication system as well as medical science. t4]
c) What is the highest order spectrum, which may be seen with monochromatic light of
wavelength 559nm, by means of a diffraction grating with 15000 lines/inch? t4]
5. a) State and explain the theory and resolving power of a plane transmission gating. t5]
b) What do you mean by plane polarized light? Explain the phenomenon of double
refraction in crystal. ll+41
 ,'i
..

c) Calculate the polarizing argle for light tavellingfum water of refractive index 1.34 I

to glass of refractive index 1.52. t4l

-tl

Grour C
i

6. a) Define the term electric dipole. Calculate the potential at a point along the axis of the
quadnrpole. [1+4]
b) Explain the principle of parallel plate capacitor and detennine its capacitance. t4I
c) [f a copper wire is compressed to make 0.5 percent shorter. What is the percelrtage
change in resistance? t4l
7. a) Define the terms conductance and resistivity. Explain the atomic view of Ohm's lanr.
i

Also write dowu the limitations of Ohms law. t6l

b) What is differe,nce between intrinsic and extinsic semiconductor. Derive the relation
conductivity of semiconductor. t3l
c) Two small spheres of charge 14 micro coulomb and 35 micro coulomb placed 20cm
.Eind.thp location of a point betweeir them where the 'field strurgth is zero.
.?p?,rt. t4I I

8. a) What is eagnetic flux densitfl Derive an expression for magnetic flrx a*rity insitle
a long solenoid, carrying current I, at a point near its ce,nter. [1+4]'
b) Prove that magnetic eaergJ density is directly proportional ti the square of the 1

magn€tic flux density, i: t4l

c) A copper skip 2cm wide and 1.5mm thick is ptaced in a magnetic field with magnetic
strength 2.6 Tesla. If a current of 145A is set up in the strip, what llall potential
difference appears zrcross the strip? The nrmber of charges is 8.4xldt per meter cube. l4l

Group D
9. a) What is meant by LC oscillation? Derive the differential equation of an LC
also calculate the frequency of LC oscillation.

b) Derive the Ma:rwell's gquations'in"diffbrential form also explains their

sigmficance. :

c) UsingMa:rwell's equationprove that (E/B) = g.

10. a) Define poynthg vector and show that S = (l/po)e, s where symbols carry their usual
meanings. : tsl
b) What is displacement current? Prove that the displacemeo.t current density in a

parallel capacitor can be written ., i =., +. t3I

dt
c) .What should be the capacitance of a capacitor in a tuned circuit of frequency 10 MIIZ
having aD inductarce of 0.01 rnH? Theresistance of the circuit is uegligible. t4]