Electro Magnetic Field
Electro Magnetic Field
Electro Magnetic Field
Contents
Topic
Page No.
Theory
01 - 03
Exercise - 1
04 - 12
Exercise - 2
12 - 25
Exercise - 3
26 - 35
Exercise - 4
36
Answer Key
37 - 41
Syllabus
Biot-Savarts law and Amperes law ; Magnetic field near a current-carrying
straight wire, along the axis of a circular coil and inside a long straight
solenoid ; Force on a moving charge and on a current-carrying wire in a
uniform magnetic field. Magnetic moment of a current loop; Effect of a
uniform magnetic field on a current loop; Moving coil galvanometer,
voltmeter, ammeter and their conversions.
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A static charge produces only electric field and only electric field can exert a force on it.
A moving charge produces both electric field ans magnetic field and both electric field and magnetic field can
exert force on it.
A current carrying conductor produces only magnetic field and only magnetic field can exert a force on it.
2.
Magnetic charge (i.e. current) , produces a magnetic field . It can not produce electric field as net charge on
a current carrying conductor is zero. A magnetic field is detected by its action on current carrying conductors
(or moving charges) and magnetic needles (compass) needles. The vector quantity B known as MAGNETIC
INDUCTION is introduced to characterise a magnetic field . It is a vector quantity which may be defined in terms
of the force it produces on electric currents . Lines of magnetic induction may be drawn in the same way as
lines of electric field . The number of lines per unit area crossing a small area perpendicular to the direction
of the induction bring numerically equal to B . The number of lines of B crossing a given area is referred to
as the MAGNETIC FLUX linked with that area. For this reason B is also called MAGNETIC FLUX DENSITY .
3.
I d x r
0 r Idsin
0 r
dB =
or dB
,
2
4
r3
4
r
here the quantity Idl is called as current element strength.
= permeability of the medium = 0 r ; 0 = permeability of free space
r = relative permeability of the medium (Dimensionless quantity).
Unit of 0 & is NA2 or Hm1 ;
0 = 4 107 Hm1
4.
5.
6.
7.
0 qv sin
4r 2
q ( v xr )
0
In vector form it can be written as dB
4 r 3
MAGNETIC INDUCTION DUE TO AN INIFINITE ST. CONDUCTOR
0I
B=
2r
MAGNETIC INDUCTION DUE TO SEMI INIFINITE ST. CONDUCTOR
0I
B=
4 r
MAGNETIC INDUCTION DUE TO A CURRENT CARRYING STRAIGHT CONDUCTOR
0 I
B=
(cos 1 + cos 2)
4R
If the wire is very long
8.
1 2 0 then , B =
0I
2R
At its centre
B=
2R
, direction
On the axis
0 NIR 2
B=
2 x 2 R 2
3/ 2
Where x = distance of the point from the centre . It is maximum at the centre .
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9.
0 I
4R
10.
11.
N
(no. of turns per m)
2R
N = total turns
12.
R >> r
13.
14.
to the horizontal at an angle called the MAGNETIC DIP at that place , such that B = total magnetic induction of
the earth at that point.
15.
AMPERES LAW
16.
B . d I
induction B experiences a force F , given by F qV x B . There fore, if the charge moves
An electric charge 'q' moving with a velocity V through a magnetic field of magnetic
in a space where both electric and magnetic fields are
.
superposed
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17.
qB
mv
and angular velocity =
and F = qvB.
(b) When v is | to B : Motion will be in circular path with radius R =
qB
m
mv sin
and pitch
(c) When v is at to B : Motion will be helical with radius Rk =
PH =
18.
qB
2mv cos
and F = qvBsin.
qB
F I ( L B)
I = current in the straight conductor
Note : In general force is F I (d B)
19.
(i)
(ii)
When two long straight linear conductors are parallel and carry a current in each , they
magnetically interact with each other , one experiences a force. This force is of :
Repulsion if the currents are anti-parallel (i.e. in opposite direction) or
Attraction if the currents are parallel (i.e. in the same direction)
II
This force per unit length on either conductor is given by F = 0 1 2 . Where r = perpendicular distance
2 r
between the parallel conductors
20.
When A = area vector outward from the face of the circuit where the current is anticlockwise,
B = magnetic induction of the uniform magnetic feild. M = magnetic moment of the current circuit = IN A
Note : This expression can be used only if B is uniform otherwise calculus will be used.
21.
22.
23.
1.
2.
24.
q
& its
2
magnetic moment is M = IR2 = 1/2qR2.
NOTE : The rate of magnetic moment to Angular momentum of a uniform rotating object which is charged uniformly
is always a constant. Irrespective of the shape of conductor M/L = q/2m
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A-2.
Two identical short magnetic dipoles of magnetic moments 1.0 A-m 2 each, placed at a separation of 2
m with their axes perpendicular to each other. The resultant magnetic field at a point midway between
the dipole is:
2m
(A) 5 107 T
A-3.
(B)
5 107 T
(C) 107 T
(D) 2 107 T
A point charge is moving in a circle with constant speed. Consider the magnetic field produced by the charge
at a fixed point P (not centre of the circle) on the axis of the circle.
(A) it is constant in magnitude only
(B) it is constant in direction only
(C) it is constant in direction and magnitude both
(D) it is not constant in magnitude and direction both.
Two infinitely long, thin, insulated, straight wires lie in the x-y plane along the x and y-axis respectively.
Each wire carries a current I, respectively in the positive x-direction and positive y-direction. The magnetic
field will be zero at all points on the straight line:
(A) y = x
B-2.
(B) y = x
(C) y = x 1
(D) y = x + 1
A current carrying wire is placed in the grooves of an insulating semi circular disc of radius 'R', as
shown. The current enters at point A and leaves from point B. Determine the magnetic field at point D.
(A)
0 I
8 R 3
(B)
0 I
4 R 3
(C)
3 0 I
4 R
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B-3.
Determine the magnitude of magnetic field at the centre of the current carrying wire arrangement
shown in the figure. The arrangement extends to infinity. (The wires joining the successive squares are
along the line passing through the centre)
(A)
0 i
(B) 0
(C)
2 a
2 2 0 i
ln2
a
SECTION (C) : MAGNETIC FIELD DUE TO A CIRCULAR LOOP, A STRAIGHT WIRE AND CIRCULAR ARC, CYLINDER, LARGE SHEET, SOLENOID, TOROID AND AMPERES LAW
C-1.
A current carrying wire AB of the length 2R is turned along a circle, as shown in figure. The magnetic field
at the centre O.
i
0 i 2
(A)
2R 2
C-2.
(B)
0 i 2
2R 2
(C)
0i
(2 )
2R
(D)
0i
(2 + )2
2R
A battery is connected between two points A and B the circumference of a uniform conducting ring of
radius r and resistance R. One of the arcs AB of the ring subtends an angle at the centre. The value
of the magnetic induction at the centre due to the current in the ring is:
A wire is wound on a long rod of material of relative permeability r = 4000 to make a solenoid. If the current
through the wire is 5 A and number of turns per unit length is 1000 per metre, then the magnetic field inside
the solenoid is :
(A) 25.12 mT
(B) 12.56 m T
(C) 12.56 T
(D) 25.12 T
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C-4.
C-5.
A coaxial cable is made up of two conductors. The inner conductor is solid and is of radius R1 & the
outer conductor is hollow of inner radius R2 and outer radius R3. The space between the conductors is
filled with air. The inner and outer conductors are carrying currents of equal magnitudes and in opposite
directions. Then the variation of magnetic field with distance from the axis is best plotted as:
(A)
(B)
(C)
(D)
Axis of a solid cylinder of infinite length and radius R lies along y-axis it carries a uniformly
R
R
distributed current i along +y direction. Magnetic field at a point , y, is :2
2
(A)
C-6.
0i
0i
( i k ) (B)
( j k )
4R
2 R
(C)
0i
j
4R
(D)
0i
( i k )
4R
Figure shows an amperian path ABCDA. Part ABC is in vertical plane PSTU while part CDA is in
horizontal plane PQRS. Direction of circumlation along the path is shown by an arrow near point B and at D.
oB . d for this path according to Amperes law will be :
(B) ( i1 + i2)0
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(C) i30
C-7.
A cylindrical wire of radius R is carrying current i uniformly distributed over its cross-section. If a
circular loop of radius ' r ' is taken as amperian loop, then the variation value of
(A)
B d
(B)
R
(C)
B d
R
B d
(D)
B d
Which of the following particles will experience minimum magnetic force (magnitude) when projected with
the same velocity perpendicular to a magnetic field?
(A) Be +++
(B) proton
(C) -particle
(D) Li++
D-2.
Electric current i enters and leaves a square loop made of homogeneous wire of uniform cross-section
through diagonally opposite corners. A charge particle q moving along the axis of the square loop. Passes
through centre at speed . The magnetic force acting on the particle when it passes through the centre has
a magnitude
(A) q
D-3.
0i
2a
(B) q
0 i
2a
(C) q
0i
a
(D) zero
Two particles X and Y having equal charges, after being accelerated through the same potential difference,
enter a region of uniform magnetic field and describe circular paths of radii R1 and R2 respectively. The
ratio of the masses of X to that of Y.
R1
(A)
R2
1/ 2
R2
(B) R
1
R1
(C)
R2
R1
(D) R
2
D-4.
A negative charged particle falling freely under gravity enters a region having uniform horizontal magnetic field pointing towards north. The particle will be deflected towards
(A) East
(B) West
(C) North
(D) South
D-5.
A proton of mass m and charge q enters a magnetic field B with a velocity v at an angle with the direction
of B. The radius of curvature of the resulting path is
(A)
D-6.
mv
qB
(B)
mv sin
qB
mv
(C) qB sin
(D)
mv cos
qB
A current I flows along the length of an infinitely long, straight, thin walled pipe. Then
(A) the magnetic field at all points inside the pipe is the same, but not zero
(B) the magnetic field at any point inside the pipe is zero
(C) the magnetic field is zero only on the axis of the pipe
(D) the magnetic field is different at different points inside the pipe.
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D-7.*
H+, He+ and O2+ all having the same kinetic energy pass through a thin region in which there is a
uniform magnetic field perpendicular to their velocity. The masses of H+, He+ and O2+ are 1 amu, 4amu
and 16 amu respectively, then
(A) H+ will be deflected most
(B) O2+ will be deflected most
(C) He+ and O2+ will be deflected equally
(D) All will be deflected equally
D 8.*
A beam of electrons moving with a momentum p enters a uniform magnetic field of flux density B
perpendicular to its motion. Which of the following statement(s) is (are) true?
p2
2m
p
Be
m
p
E-2.*
E-3.*
E-4.*
A positively charged particle moves in a region having a uniform magnetic field and uniform electric field in
same direction. At some instant, the velocity of the particle is perpendicular to the field direction. The path of
the particle will be
(A) a straight line
(B) a circle
Two ions have equal masses but one is singly-ionized and other is tripply-ionized. They are projected from
the same place in a uniform magnetic field with the same velocity perpendicular to the field.
(A) Both ions will go along circles of equal radii.
(B) The circle described by the single-ionized charge will have a radius tripply that of the other circle
(C) The two circles do not touch each other
(D) The two circles touch each other
E-5.*
A positively charged particle is moving along the positive X-axis. You want to apply a magnetic field for a short
time so that the particle may reverse its direction and move parallel to the negative X-axis. This can be done
by applying the magnetic field along.
(A) Y-axis
(B) Z-axis
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A conducting circular loop of radius r carries a constant current i. It is placed in a uniform magnetic field
B such that B is perpendicular to the plane of the loop. The magnetic force acting on the loop is
(A) i r B
F-2.
(B) 2 r i B
(C) zero
A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel
to one of the sides of the loop and the plane of the loop is same of the left wire. If a steady current I is
established in the wire as shown in the (fig) the loop will -
F-3.
(D) r i B
(A)
F-4.
(B)
2 ( i j k )
(C)
(D)
2 ( i j k )
2 ( i j k )
F-5.
2 ( i j k )
0i 2
b
(B)
0i 2
2 b
(C)
0i
2 b
(D)
0i
2 b 2
In the figure shown a current 1 is established in the long straight wire AB. Another wire CD carrying current
2 is placed in the plane of the paper. The line joining the ends of this wire is perpendicular to the wire AB. The
resultant force on the wire CD is:
(A) zero
(C) towards positive y-axis
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SECTION (G) : MAGNETIC FORCE AND TORQUE ON A CURRENT CARRYING LOOP AND
MAGNETIC DIPOLE MOMENT
G-1.
A bar magnet has a magnetic moment 2.5 JT 1 and is placed in a magnetic field of 0.2 T. Work done in
turning the magnet from parallel to antiparallel position relative to the field direction.
(A) 0.5 J
(B) 1 J
(C) 2.0 J
(D) Zero
G-2.
A circular loop of area 1 cm2, carrying a current of 10 A, is placed in a magnetic field of 0.1 T perpendicular
to the plane of the loop. The torque on the loop due to the magnetic field is
(A) zero
(B) 10-4 N-m
(C) 102 N-m
(D) 1 N-m
A power line lies along the east-west direction and carries a current of 10 ampere. The force per metre
due to the earth's magnetic field of 104 T is
(A) 105 N
(B) 104 N
(C) 103 N
(D) 102 N
H-2.
A circular coil of radius 20 cm and 20 turns of wire is mounted vertically with its plane in magnetic
meridian. A small magnetic needle (free to rotate about vertical axis) is placed at the center of the coil.
It is deflected through 45 when a current is passed through the coil and in equilibrium (Horizontal
component of earth's field is 0.34 104 T). The current in coil is:
(A)
17
A
10
(B) 6A
(C) 6 103 A
(D)
3
A
50
SECTION () : MISCELLENEOUS
-1.
(D) Ferromagnetic
a
b
a,b
c
c,d
1.
(B) b
(C) c
(D) d
Which wire has the greatest magnitude of the magnetic field on the surface ?
(A) a
3.
2.
a,c
b,d
(B) b
(C) c
(D) d
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Column-II gives four situations in which three (in q,r,s) and four (in p) semi infinite current carrying wires are
placed in xy-plane as shown. The magnitude and direction of current is shown in each figure. Column-I gives
statements regarding the x and y components of magnetic field at a point P whose coordinates are P (0, 0,
d). Match the statements in column-I with the corresponding figures in column-II and indicate your answer
by darkening appropriate bubbles in the 4 4 matrix given in OMR.
Column-I
Column-II
(p)
(q)
(r)
point P is
0 i
in
4d
5.
(s)
0 i
in
2d
There are four situations given in column involving a magnetic dipole of dipole moment placed in uniform
external magnetic field B . Column gives corresponding results. Match the situtations in column with the
corresponding results in column
Column -
Column -
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6.
& uniform
By = Bz = Ex = Ez = 0
u= 0
(P)
(Q)
(ii)
E = 0 ; u x B x + u yB y u z B z
(R)
circle
helix with uniform pitch
and constant radius
cycloid
(S)
(iii)
u x B 0, u xE 0
(iv)
u B, B ||E
unknown curve
(U)
(V)
2.
Two parallel, long wires carry currents i1 and i2 with i1 > i2. When the current are in the same direction, the
magnetic field at a point midway between the wire is 20T. If the direction of i1 is reversed, the field becomes
30T. The ratio i1/i2 is
(A) 4
3.
(B) 3
(C) 5
(D) 1
Consider a long, straight wire of cross-section area A carrying a current i. Let there be n free electrons per
unit volume. An observer sitting in the car moving in the same direction to the current with a speed = (i/nAe)
and separated from the wire by a distance r. The magnetic field seen by the observer is
(A)
0i
2 r
(B) zero
(C)
0i
r
(D)
20i
r
4.
A long, straight wire carries a current along the Z-axis. One can not find two points in the X-Y plane such that
(A) the magnetic fields are equal in magnitude and same in direction
(B) the directions of the magnetic fields are the same
(C) the magnitudes of the magnetic fields are equal
(D) the field at one point is opposite to that at the other point.
5.
A vertical wire carries a current in downward direction. An electron beam sent horizontally towards the wire
will be deflected (gravity free space)
(A) towards right
(C) upwards
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(D) downwards
6.
A current-carrying, straight wire is kept along the axis of a square loop carrying a current. The straight wire
(A) will exert an inward force on the square loop
(B) will exert an outward force on the squareloop
(C) will not exert any force on the square loop
(D) will exert a force on the square loop parallel to itself.
7.
A proton beam is going from west to east and an electron beam is going from east to west. Neglecting the
earths magnetic field, the electron beam will be deflected
(A) towards the proton beam
(B) away from the proton beam
(C) away from the electron beam
(D) None of these
8.
A proton is moved along a magnetic field line. The magnetic force on the particle is
(A) along its velocity
(B) opposite to its velocity
(C) perpendicular to its velocity
(D) zero.
9.
Two parallel wires carry currents of 10 A and 40 A in opposite directions. Another wire carrying a current
antiparallel to 20 A is placed midway between the two wires. The magnetic force on it will be
(A) towards 20 A
(B) towards 40 A
(C) zero
(D) perpendicular to the plane of the currents
10.
A toroid of mean radius ' a ' , cross section radius ' r ' and total number of turns N. It carries a current ' i '. The
torque experienced by the toroid if a uniform magnetic field of strength B is applied :
(A) is zero
(B) is B i N r2
(C) is B i N a2
(D) depends on the direction of magnetic field.
11.
A long, thick straight conductor of radius R carries current uniformly distributed in its cross section area.
The ratio of energy density of the magnetic field at distance R/2 from surface inside the conductor and
outside the conductor is:
(A) 1: 16
(B) 1: 1
(C) 1: 4
(D) 9/16
12.
A steady current 'l' flows in a small square loop of wire of side L in a horizontal plane. The loop is now
folded about its middle such that half of it lies in a vertical plane. Let 1 and 2 respectively denote the
magnetic moments of the current loop before and after folding. Then :
(A) 2 = 0
(C) 2
2
1
1
(D)
2
2
13.
A proton of mass 1.67 1027 kg and charge 1.6 1019 C is projected with a speed of 2 106 m/s at an
angle of 60 to the x-axis. If a uniform magnetic field of 0.104 T is applied along the y-axis, the path of
the proton is :
(A) A circle of radius 0.2 m and time period 107 s
(B) A circle of radius 0.1 m and time period 2 107 s
(C) A helix of radius 0.1 m and time period 2 107 s
(D) A helix of radius 0.2 m and time period 4 107 s
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The magnetic field at the origin due to a current element i d placed at a position r is
0i d l xr
(A)
4 r 3
15.*
(B)
i
0
4
r d
0i r d
(C)
4 r 3
r3
1
(D)
i
0
4
d r
r3
00
tance and R is a resistance. All other symbols have standard meanings
(A) x, y have the same dimensions.
(B) y, z have the same dimensions
(C) z, x have the same dimensions
(D) one of the three pairs have the same dimensions
16.*
A hollow tube is carrying an electric current along its length distributed uniformly over its surface. The
magnetic field
(A) increases linearly from the axis to the surface
(B) is constant inside the tube
(C) is zero at the axis
(D) is non-zero outside the tube at finite distance from surface
17.*
In a coaxial, straight cable, the central conductor and the outer conductor carry equal currents in opposite
directions. The magnetic field is non-zero.
A particle of charge +q and mass m moving under the influence of a uniform electric field E i and a
uniform magnetic field B k follows a trajectory from P and Q as shown in figure. The velocities at P and
Q are v i and 2v j . Which of the following statement(s) is/are correct?
y
E
P
v
B
a
2a
2v
Q
3 mv 2
(A) E = 4 qa
3 mv 3
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19.*
Let E and B denote the electric and magnetic fields in a certain region of space. A proton moving with
a velocity v along a straight line enters the region and is found to pass through it undeflected. Indicate
which of the following statements are possible for the observation:
(A) E = 0 and B = 0
(B) E 0 and B = 0
The magnetic moment of a short dipole is, 1 A m 2. What is the magnitude of the magnetic induction
in air at 10 cm from centre of the dipole on a line making an angle of 30 from the axis of the dipole?
2.
A point charge q = 2C is at the origin. It has velocity 2 i m/s. Find the magnetic field at the following points
in vector form (at the moment when the charged particle passes through the origin) :
(i) (2, 0, 0)
(ii) (0, 2, 0)
(iii) (0, 0, 2)
(iv) (2, 1, 2)
(v) Is the magnitude of the magnetic field on the circumference of the circle (in yz plane) y2 + z2 = c2 where c
is a constant is same every where. Is it same in direction also.
(vi) Answer the above (v) for the circle of same equation but in a plane x = a where a is a constant.
3.
A particle of negative charge of magnitude q is revolving with constant speed ' V' in a circle of radius R as
shown in figure. Find the magnetic field (magnitude and direction) at the following points :
A pair of stationary and infinitely long bent wires is placed in the X-Y plane as shown in figure. The
wires carry currents of 10A each as shown. The segments L and M are along the x-axis. The segments
P and Q are parallel to the Y - axis such that OS = OR = 0.02 m. Find the magnitude and direction
of the magnetic induction at the origin O.
5.
A current of 1 amp is flowing in the sides of an equilateral triangle of side 4.5 x 10 -2 m. Find the
magnetic field at the centroid of triangle.
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6.
Two straight infinitely long and thin parallel wires are spaced 0.1 m apart and carry a current of 10
ampere each. Find the magnetic field at a point distant 0.1 m from both wires in the two cases when
the currents are in the
(i) Same and
(ii) Opposite direction.
7.
Four infinitely long 'L' shaped wires, each carrying a current i have been arranged as shown in the
figure. Obtain the magnetic field strength at the point 'O' equidistant from all the four corners.
8.
Figures shows a long wire bent at the middle to form a right angle. Show that the magnitudes of the magnetic
fields at the points Q and R are unequal and find these magnitudes. The wire w1 and the circumference of
circle are coplaner and w2 is perpendicular to plane of paper. Also find the ratio of field at Q and R
9.
A long wire carrying a current i is bent to form a plane angle . Find the magnetic field B at a point on the
bisector of this angle situated at a distance x from the vertex is written in the form of K cot
the value of K.
10.
Find the magnetic field B at the centre of a square loop of side 'a', carrying a current i.
11.
Each of the batteries shown in figuer has an emf equal to 10 V. Find the magnetic field B at the point p.
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12.
(i)
(ii)
Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 1 A. The coils have 50 and 100
turns respectively and are placed in such a way that their planes as well as the centre coincide. Find
the magnitude of the magnetic field B at the common centre when the currents in the coils are (a) in
the same sense (b) in the opposite sense.
If the outer coil of the above problem is rotated through 90 about a diameter, what would be the
magnitude of the magnetic field B at the centre?
13.
Two circular coils of wire each having a radius of 4 cm and 10 turns have a common axis and are 6 cm
apart. If a current of 1 A passes through each coil in the opposite direction find the magnetic induction.
(a) At the centre of each coil ;
(b) At a point on the axis, midway between them.
14.
Two wire loops PQRSP formed by joining two semicircular wires of radii R1 and R2 carries a current I as
shown in (fig.) The magnitude of the magnetic induction at the center C is.....
I
R2
R1
15.
Find the magnitude of the magnetic induction B of a magnetic field generated by a system of thin
conductors (along which a current i is flowing) at a point A (0, R, 0), that is the centre of a circular
conductor of radius R. The circular part is in yz plane.
16.
Find the magnetic induction of the field at the point O of a loop with current , whose shape is
illustrated in figure
(a)
(b)
(c)
In figure 'a' the radii a and b, as well as the angle are known,
In figure b, the radius a and the side b are known.
A current = 5.0 A flows along a thin wire shaped as shown in figure. The radius of a curved part
of the wire is equal to R = 120 mm, the angle 2 = 90. Find the magnetic induction of the field
at the point O.
0
2
2
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17.
Find the magnetic induction at the point O if the wire carrying a current has the shape shown in figure
a, b, c. The radius of the curved part of the wire is R, the linear parts of the wire are very long.
z
(a)
(b)
(c)
18.
A conductor consists of an infinite number of adjacent wires, each infinitely long & carrying a current i.
Show that the lines of B will be as represented in figure & that B for all points in front of the infinite
current sheet will be given by, B = (1/2)0 ni, where n is the number of conductors per unit length.
19.
Figure shows a cylindrical conductor of inner radius a & outer radius b which carries a current i uniformly spread over its cross section. Show that the magnetic field B for points inside the body of the
r 2 a2
conductor (i.e. a < r < b) is given by, B =
. Check this formula for the limiting case
r
2 (b 2 a 2 )
of a = 0.
0i
20.
A thin but long, hollow, cylindrical tube of radius r carries a current i along its length. Find the magnitude of
the magnetic field at a distance r/4 from the surface (a) inside the tube (b) outside the tube.
21.
The magnetic field B inside a long solenoid, carrying a current of 10 A, is 3.14 102 T. Find the number of
turns per unit length of the solenoid.
22.
A copper wire having resistance 0.01 ohm in each metre is used to wind a 400 turn solenoid of radius 1.0 cm
and length 20 cm. Find the emf of a battery which when connected across the solenoid will cause a magnetic
field of 1.0 102 T near the centre of the solenoid.
23.
A charged particle is accelerated through a potential difference of 24 kV and acquires a speed of 2106 m/s.
It is then injected perpendicularly into a magnetic field of strength 0.2 T. Find the radius of the circle described
by it.
24.
A neutron, a proton, an electron and an -particle enters a uniform magnetic field with equal velocities.
The field is directed along the inward normal to the plane of the paper. Which of these tracks followed
are by electron and -particle.
ETOOSINDIA.COM
25.
In the formula X = 3 YZ2, the quantities X and Z have the dimensions of capacitance and magnetic
induction respectively. The dimensions of Y in the MKS system are..............
26.
Two long parallel wires carrying currents 2.5 amps and I amps in the same direction (directed into the
plane of the paper) are held at P and Q respectively such that they are perpendicular to the plane of
paper. The points P and Q are located at a distance of 5m and 2m respectively from a collinear point R.
(a)
(b)
27.
An particle is accelerated by a potential difference of 104V. Find the change in its direction of motion,
if it enters normally in a region of thickness 0.1 m having transverse magnetic induction of 0.1 Tesla.
(Given: mass of -particle is equal to 6.4 1027 kg)
28.
A magnetic field of 8 k mT exerts a force of (4.0 i + 3.0 j ) 1010 N on a particle having a charge of
5 1010 C and going in the X Y plane. Find the velocity of the particle.
29.
30.
A particle having a charge of 2.0 108 C and a mass of 2.0 1010 g is projected with a speed of 2.0 103
m/s in a region having a uniform magnetic field (B = 0.1 T). Find the radius of the circle formed by the particle
and also the frequency.
31.
A proton describes a circle of radius 1 cm in a magnetic field of strength 0.10 T. What would be the radius of
the circle described by an deuterium moving with the same speed in the same magnetic field?
32.
An electron having a kinetic energy of 400 eV circulates in a path of radius 20 cm in a magnetic field. Find the
magnetic field and the number of revolutions per second made by the electron.
33.
A proton is projected with a velocity of 3 106 m/s perpendicular to a uniform magnetic field of 0.6T. Find the
acceleration of the proton. mass of proton =
34.
(a)
(b)
An electron moves along a circle of radius 1 m in a perpendicular magnetic field of strength 0.50 T.
What would be its speed? Is it reasonable?
If a proton moves along a circle of the same radius in the same magnetic field, what would be its
speed? mass of proton =
35.
5
10 27 kg
3
5
10 27 kg
3
A particle of mass m and positive charge q, moving with a uniform velocity v, enters a magnetic field B as
shown in figure. (a) Find the radius of the circular arc it describes in the magnetic field. (b) Find the angle
subtended by the arc at the centre. (c) How long does the particle stay inside the magnetic field? (d) Solve
the three parts of the above problem if the charge q on the particle is negative.
v /4
ETOOSINDIA.COM
36.
A particle of mass m and charge q is projected into a region having a perpendicular magnetic field B. Find the
angle of deviation (figure) of the particle as it comes out of the magnetic field if the width d of the region is very
slightly smaller than
(a)
37.
mv
qB
mv
(b)
2qB
(c)
3mv
qB
Figure shows a convex lens of focal length 10 cm lying in a uniform magnetic field B of magnitude 1.2 T
parallel to its principal axis. A particle having a charge 2.0 103 C and mass 2.0 105 kg is projected
perpendicular to the plane of the diagram with a speed of 4.8 m/s. The particle moves along a circle with its
centre on the principal axis at a distance of 15 cm from the lens. The axis of the lens and of the circle are
same. Show that the image of the particle goes along a circle and find the radius of that circle.
B
P
38.
A particle having a charge of 5.0 C and a mass of 5.0 1012 kg is projected with a speed of 1.0 km/s
in a magnetic field of magnitude 5.0 mT. The angle between the magnetic field vector and the velocity vector
is sin1 (0.90). Show that the path of the particle will be a helix. Find the diameter of the helix and its pitch.
39.
A proton projected in a magnetic field of 0.04 T travels along a helical path of radius 5.0 cm and pitch 20 cm.
Find the components of the velocity of the proton along and perpendicular to the magnetic field. Take the
mass of the proton = 1.6 1027 kg.
40.
An electron beam passes through a magnetic field of 2 103 Wb/m2 and an electric field of 3.2 104 V/m,
both acting simultaneously. ( E B V ) If the path of electrons remains undeflected calculate the speed of
the electron. If the electric field is removed, what will be the radius of the electron path
[mass of electron = 9.1 1031 kg]?
41.
If two charged particles of same mass and charge are describing circles in the same magnetic field
with radii r1 and r2 (> r1), the speed of the first particle is.... that of the second particle while the time
period of the particle is...... that of the second particle.
42.
A conducting wire of length , lying normal to a magnetic field B, moves with a velocity v as shown in figure.
(a) Find the average magnetic force on a free electron of the wire. (b) Due to this magnetic force, electrons
concentrate at one end resulting in an electric field inside the wire. The redistribution stops when the electric
force on the free electrons balances the magnetic force. Find the electric field developed inside the wire when
the redistribution stops. (c) What potential difference is developed between the ends of the wire?
ETOOSINDIA.COM
43.
A current i is passed through a cylindrical gold strip of radius r. The number of free electrons per unit volume
is n. (a) Find the drift velocity v of the electrons. (b) If a magnetic field B exists in the region as shown in
figure, what is the average magnetic force on the free electrons? (c) Due to the magnetic force, the free
electrons get accumulated on one side of the conductor along its length. This produces a transverse electric
field in the conductor which opposes the magnetic force on the electrons. Find the magnitude of the electric
field which will stop further accumulation of electrons. (d) What will be the potential difference developed
across the width of the conductor due to the electron accumulation? The appearance of a transverse emf,
when a current-carrying wire is placed in a magnetic field, is called Hall effect.
44.
A uniform magnetic field of magnitude 0.20 T exists in space from east to west. A particle having mass 105
kg and charge 105 C is projected from south to north so that it moves with a uniform velocity. Find velocity of
projection of the particle? (g = 10 m/s2)
45.
A particle moves in a circle of radius 1.0 cm under the action of a magnetic field of 0.40 T. An electric field of
200 V/m makes the path straight. Find the charge/mass ratio of the particle.
46.
A proton goes undeflected in a crossed electric and magnetic field (the fields are perpendicular to each
other) at a speed of 10 5 m/s. The velocity is perpendicular to both the fields. When the electric field is
switched off, the proton moves along a circle of radius 2 cm. Find the magnitudes of the electric and
the magnetic fields. Take the mass of the proton = 1.6 1027 kg.
47.
A particle having mass m and charge q is released from the origin in a region in which electric field and
magnetic field are given by
B B 0 j and E E 0 i .
Find the speed of the particle as a function of its X-coordinate.
48.
Consider a 10 cm long portion of a straight wire carrying a current of 10 A placed in a magnetic field of 0.1 T
making an angle of 37 with the wire. What magnetic force does the wire experience?
49.
A current of 2 A enters at the corner d of a square frame abcd of side 10 cm and leaves at the opposite corner
b. A magnetic field B = 0.1 T exists in the space in direction perpendicular to the plane of the frame as shown
in figure. Find the magnitude and direction of the magnetic forces on the four sides of the frame.
50.
A magnetic field of strength 1.0 T is produced by a strong electromagnet in a cylindrical region of diameter
4.0 cm as shown in figure. A wire, carrying a current of 2.0 A, is placed perpendicular to and intersecting the
axis of the cylindrical region. Find the magnitude of the force acting on the wire.
S
N
ETOOSINDIA.COM
51.
A wire of length l carries a current i along the y-axis. A magnetic field exists which is given as B B 0 ( i j k )T .
52.
53.
A thin straight horizontal wire of length 0.2 m whose mass is 104 kg floats in a magnetic induction field
when a current of 10 ampere is passed through it. To make this possible, what should be the minimum
magnetic strength?
(Take g = 10 m/s 2)
54.
Two long straight parallel conductors are separated by a distance of r1 = 5cm and carry constant
currents i1 = 10 A & i2 = 20 A. What work per unit length of a conductor must be done to increase the
separation between the conductors to r2 = 10 cm if, currents flow in the same direction?
55.
2
x . A uniform magnetic
A wire, carrying a current, i, is kept in the X Y plane along the curve y = A sin
field B exists in the z-direction. Find the magnitude of the magnetic force on the portion of the wire between
x = 0 and x = /2
56.
A rigid wire consists of a semicircular portion of radius R and two straight sections (figure). The wire is
partially immersed in a perpendicular magnetic field B as shown in the figure. Find the magnetic force on the
wire if it carries a current i.
57.
A metal wire PQ of mass 10 gm lies at rest on two horizontal metal rails separated by 4.90 cm (figure). A
vertically downward magnetic field of magnitude 0.800 T exists in the space. The resistance of the circuit is
slowly decreased and it is found that when the resistance goes below 20.0 , the wire PQ starts sliding on
the rails. Find the coefficient of friction. Neglect magnetic force acting on wire PQ due to metal rails (g = 9.8
m/s2)
6V
58.
B B 0 1 k , where B0 and are constants, X is the X coordinate of a point and k is the unit vector along
Z axis.
A square loop of edge and carrying a current i, is placed with its edges parallel to the X, Y axes. Find the
magnitude of the net magnetic force experienced by the loop.
ETOOSINDIA.COM
59.
Two parallel wires separated by a distance of 10 cm carry currents of 20 A and 80 A along the same direction.
Where should a third current carrying wire be placed so that it experiences no magnetic force?
60.
Figure shows a part of an electric circuit. The wires AB, CD and EF are very long and have identical resistances. The separation between the neighboring wires is 2 cm. The wires AE and BF have negligible resistance and the ammeter reads 60 A. Calculate the magnetic force per unit length on AB and CD.
61.
A straight, long wire carries a current of 20 A. Another wire carrying equal current is placed parallel to it. If the
force acting on unit length of the second wire is 2.0 104 N, what is the separation between them?
62.
A circular coil of 100 turns has an effective radius 0.05 m and carries a current of 0.1 amp. How much
work is required to turn it in an external magnetic field of 1.5 wb/m 2 through 1800 about an axis perpendicular to the magnetic field. The plane of the coil is initially perpendicular to the magnetic field.
63.
(a)
A circular loop of radius a, carrying a current i, is placed in a two-dimensional magnetic field. The
centre of the loop coincides with the centre of the field (figure). The strength of the magnetic field at
the periphery of the loop is B. Find the magnetic force on the wire.
(b)
A hypothetical magnetic field existing in a region is given by B B 0 er , where e r denotes the unit
vector along the radial direction of a point relative to the origin and B0 = constant. A circular loop of
radius a, carrying a current i, is placed with its plane parallel to the X-Y plane and the centre at (0,
0, a). Find the magnitude of the magnetic force acting on the loop.
64.
A rectangular coil of 100 turns has length 4 cm and width 5 cm. It is placed with its plane parallel to a uniform
magnetic field and a current of 2A is sent through the coil. Find the magnitude of the magnetic field B, if the
torque acting on the coil is 0.2 N-m.
65.
A 50-turn circular coil of radius 4 cm carrying a current of 2.5 A is rotated in a magnetic field of strength 0.20
T. (a) What is the maximum torque that acts on the coil? (b) In a particular position of the coil, the torque
acting on it is half of this maximum. What is the angle between the magnetic field and the plane of the coil?
66.
A square loop of sides 10 cm carries a current of 10 A. A uniform magnetic field of magnitude 0.20 T exists
parallel to the longer side of the loop. (a) What is the force acting on the loop? (b) What is the torque acting
on the loop?
67.
A circular coil of diameter 2.0 cm has 500 turns in it and carries a current of 1.0 A. Its axis makes an angle
of 30 with the uniform magnetic field of magnitude 0.40 T that exists in the space. Find the torque acting on
the coil.
68.
A circular loop carrying a current i has wire of total length L. A uniform magnetic field B exists parallel to the
plane of the loop. (a) Find the torque on the loop. (b) If the same length of the wire is used to form a
rectangular loop of side ratio 1 : 2 , what would be the torque? Which is larger?
ETOOSINDIA.COM
69.
In a hydrogen atom the electron moves in an orbit of radius 0.5 making 1016 rev/s. What is the
magnetic moment associated with the orbital motion of the electron and the magnetic field at the
centre?
70.
A charge Q is spread uniformly over an insulated ring of radius R. What is the magnetic moment of the
ring if it is rotated with an angular velocity about its axis?
71.
Two circular coils each of 100 turns are held such that one lies in the vertical plane and the other in the
horizontal plane with their centres coinciding. The radius of the vertical and the horizontal coils are
respectively 20 cm and 30 cm. If the directions of the current in them are such that the earth's
magnetic field at the centre of the coil is exactly neutralized, calculate the current in each coil.
[horizontal component of the earth's field = 27.8 A m -1 (Tesla) ; angle of dip = 30]
72.
A short magnet of magnetic moment 6 Amp.m 2 is lying in a horizontal plane with its North pole
pointing 60 East of North. Find the net horizontal magnetic field at a point on the axis of the magnet
0.2 m away from it. [ Horizontal component of earth's magnetic field = 0.3 x 10 -4 tesla ]
N
N
60
E
W
S
S
73.
A coil of 50 turns and 20 cm diameter is made with a wire of 0.2 mm diameter and resistivity 2106
cm. The coil is connected to a source of EMF. 20 V and negligible internal resistance.
(a)
(b)
What must be the potential difference across the coil so as to nullify the earth's horizontal
magnetic induction of 3.14 10 -5 tesla at the centre of the coil. How should the coil be placed
to achieve the above result.
74.
A charge of 1 coulomb is placed at one end of a non-conducting rod of length 0.6m. The rod is rotated
in a vertical plane about a horizontal axis passing through the other end of the rod with an angular
velocity 104 rad/sec. Find the magnetic field at a point on the axis of rotation at a distance of 0.8m
from the centre of the path. Now half of the charge is removed from one end and placed on the other
end. The rod is rotated in a horizontal plane about vertical axis passing through the mid point of the rod
with the same angular velocity. Calculate the magnetic field at the point on the axis at a distance of
0.4m from the centre of the rod.
75.
A square loop of wire of edge a carries a current i. Show that the value of B at the center is given by,
B=
2 2 0i
.
a
76.
A circular loop of radius r carries a current i. How should a long, straight wire carrying a current 3i be placed
in the plane of the circle so that the magnetic field at the centre becomes zero?
77.
A constant direct current of uniform density j is flowing in an infinitely long cylindrical conductor. The
conductor contains an infinitely long cylindrical cavity whose axis is parallel to that of the conductor
and is at a distance from it. Determine the magnetic induction B inside the cavity..
ETOOSINDIA.COM
78.
A solenoid of length 0.4 m and diameter 0.6 m consists of a single layer of 1000 turns of fine wire
carrying a current of 5.0 103 ampere. Calculate the magnetic field strength on the axis at the middle
and at the ends of the solenoid.
79.
A charged particle +q of mass m is placed at a distance d from another charge particle 2q of mass 2
m in a uniform magnetic field of induction vector B as shown in the fig. If the particles are projected
towards each other with equal speeds v.
(a)
Find the maximum value of the projection speed Vmax so that the two particles do not collide.
(b)
Find the time interval after which collision occurs between the particles if projection speed
equals 2Vmax.
(c)
Assuming that the particles stick after the collision find the radius of the circular path of the
particle in subsequent motion. (Neglect the interaction between the particles)
80.
A straight rod of mass m and length l can slide on two parallel plastic rails kept in a horizontal plane
with a separation d. The coefficient of friction between the wire and the rails is . If the wire carries a
current i, what minimum magnetic field should exist in the space in order to slide the wire on the rails.
81.
A finite conductor AB carrying current i is placed near a fixed very long wire current carrying i0 as
shown in the figure. Find the point of application and magnitude of the net ampere force on the conductor
AB. What happens to the conductor AB if it is free to move. (Neglect gravitational field)
82.
Figure shows (only cross section) a wooden cylinder C with a mass m of 0.25 kg, a radius R and a
length perpendicular to the plane of paper of 0.1 meter with N = 10 where N is number of turns of wire
wrapped around it longitudinally, so that the plane of the wire loop contains the axis of the cylinder.
What is the least current through the loop that will prevent the cylinder from moving down a plane
whose surface is inclined at angle to the horizontal, in the presence of a vertical field of magnetic
induction 0.5 weber/meter2, if the plane of the windings is parallel to the inclined plane? (bottom most
point of cylinder does not slip)
B
C
ETOOSINDIA.COM
2.
A current carrying loop is placed in a uniform magnetic field towards right in four different orientations,
V, arrange them in the decreasing order of Potential Energy.[JEE 2003 (Screening) 3/84 ]
(i)
(ii)
(iii)
(iv)
(A) , , V
(B) , , , V
(C) , V, ,
(D) , V, ,
A conducting loop carrying a current is placed in a uniform magnetic field pointing into the plane of the
paper as shown. The loop will have a tendency to.
[JEE 2003 (Screening) 3/84 ]
(A) move along the positive x direction
(B) move along the negative x direction
(C) contract
(D) expand
3.
A proton and particle, after accelerating through same potential difference enters into a uniform magnetic
field perpendicular to their velocities, find the radius ratio of proton and particle. [JEE 2004 (Mains), 2/60]
4.
An electron traveling with a speed u along the positive x-axis enters into a region of magnetic field where
B = B0 k (x > 0). It comes out of the region with speed v then
(A) v = u at y > 0
(C) v > u at y > 0
5.
(B) v = u at y < 0
(D) v > u at y < 0
Relation for a Galvanometer having number of turns N, area of cross section A and moment of inertia is
given as : = Ki where K is a positive constant and i is current in the coil placed in the magnetic field B.
[JEE 2005 Mains, 2+2+2/60]
(i)
Find K in terms of B, N and A
(ii)
(iii)
If at an instant charge Q is flown through the galvanometer, find the maximum deflection in
the coil. (assume I as the moment of inertia of the coil )
ETOOSINDIA.COM
6.*
A magnetic field B B 0 j exists in the region a < x < 2a and B B 0 j , in the region 2a < x < 3a, where B0 is a
positive constant. A positive point charge moving with a velocity V v 0 i , where v0 is a positive constant, enters the
magnetic field at x = a. The trajectory of the charge in this region can be like.
B0
2a
3a
-B0
(A) 0
x
a
2a
3a
(B) 0
2a
3a
(C) 0
x
a
x
a
2a
(D) 0
3a
ETOOSINDIA.COM
x
a
2a
3a
8.
Two wires each carrying a steady current are shown in four configurations in Column . Some of the
resulting effects are described in Column . Match the statements in Column with the statements in
Column and indicate your answer by darkening appropriate bubbles in the 4 4 matrix given in the ORS.
[JEE - 2007' 6/162]
Column
Column
(A)
Point P is situated midway
(p)
The magnetic fields (B) at P due to the
P
(B)
(q)
direction.
The magnetic field B at P due to the
currents in the wires are in opposite
P
which have same radii.
(C)
directions.
(r)
(s)
P
which have same radii.
(D)
of the wires.
9.
A particle of mass m and charge q, moving with velocity V enters region normal to the boundary as shown
in the figure. Region has a uniform magnetic field B perpendicular to the plane of the paper. The length of
the region is . Choose the correct choice(s).
[JEE - 2008' 4/163]
qB
m
qB
m
qB
m
(D) Time spent in Region is same for any velocity V as long as the particle returns to Region
ETOOSINDIA.COM
10.
Six point charges, each of the same magnitude q, are arranged in different manners as shown in ColumnII.
In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the
electric potential at M (potential at infinity is zero) due to the given charge distribution when it is at rest. Now,
the whole system is set into rotation with a constant angular velocity about the line PQ. Let B be the
magnetic field at M and be the magnetic moment of the system in this condition. Assume each rotating
charge to be equivalent to a steady current.
[JEE - 2009, 8/160 conducted by IIT Guwahati]
ColumnI
ColumnII
(A)
E=0
(p)
(B)
V0
(q)
(C)
B=0
(r)
P
+
(D)
(s)
P
+
(t)
+
+
M
Q
11.
A steady current goes through a wire loop PQR having shape of a right angle triangle with PQ = 3x, PR =
0
4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is k 48x , find the value of k.
ETOOSINDIA.COM
12.
A thin flexible wire of length L is connected to two adjacent fixed points carries a current in the clockwise
direction, as shown in the figure. When system is put in a uniform magnetic field of strength B going into the
plane of paper, the wire takes the shape of a circle. The tension in the wire is :
[JEE 2010, 3/163, 1]
(A) BL
13.
(B)
BL
(C)
BL
2
(D)
BL
4
An electron and a proton are moving straight parallel paths with same velocity. They enter a semi-infinite
region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?
(A) They will never come out of the magnetic field region
14.
A long insulated copper wire is closely wound as a spiral of N turns. The spiral has inner radius a and
outer radius b. The spiral lies in the X-Y plane and a steady current I flows through the wire. The Zcomponent of the magnetic field at the center of the spiral
[IIT-JEE 2011; 3/160]
(A)
15.
0N
b
In
2(b a)
a
(B)
0N
ba
In
2(b a)
ba
(C)
0N
b
In
2b
a
(D)
0N
ba
In
2b
ba
Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and
magnetic fields E E0 j and B B0 j . At time t = 0, this charge has velocity in the x-y plane, making an
angle with the x-axis . Which of the following option(s) is(are) correct for time t > 0 ?
(A) If = 0 , the charge moves in a circular path in the x-z plane.
(B) If = 0, the charge undergoes helical motion with constant pitch along the y-axis.
(C) If = 10 the charge undergoes helical motion with its pitch increasing with time along the y-axis.
(D) If = 90, the charge undergoes linear but accelerated motion along the y-axis.
ETOOSINDIA.COM
16.
A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the
cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of
the magnetic field at the point P is given by
17.
18.
N
aJ, then the value of N is ?
12 0
A loop carrying current I lies in x-y plane as shown in the figure. The unit vector k is coming out of the plane
of the paper. The magnetic moment of the current loop is
[IIT-JEE 2012; 3/136, 1]
(A) a2 I k
(B) 1 a2 I k
2
(C) 1 a2 I k
2
(D) (2+1)a2 I k
An infinitely long hollow conducting cylinder with inner radius R/2 and outer radius R carries a unifrom current
density along its length. The magnitude of the magnetic field, B as a function of the radial distance r from
the axis is best represented by
(A)
(B)
(C)
(D)
ETOOSINDIA.COM
19.
1 , enters a region of
u1 4ims
uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x = 0 to x = L
for all values of y. After passing through this region, the particle emerges on the other side after 10 milliseconds
with a velocity u2
50M
units
3Q
20.
100M
units
3Q
A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is
placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries
a steady current I. Consider a point P at a distance r form the common axis. The correct statement (s) is
(are)
[JEE Advanced (P-2) 2013]
(A) In the region 0 < r < R, the magnetic field is non-zero.
(B) In the region R < r < 2R, the magnetic field is along the common axis.
(C) In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis.
(D) In the region r > 2R, the magnetic field is non-zero.
A magnetic needle lying parallel to a magnetic field requires W units of work to turn it through 60. The torque
needed to maintain the needle in this position will be :
[AIEEE 4/300 2003]
(1)
3W
(2) W
(3) ( 3 / 2) W
(4) 2 W
2.
3.
A current i ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any
point inside the tube is :
[AIEEE 4/300 2004]
(1) infinite vuUr
4.
(3)
0 2i
, tesla
4 r
(4)
2i
tesla
r
A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of
the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of the coil will be:
[AIEEE 4/300 2004]
(1) nB
(2) n2B
(3) 2nB
(4) 2n2B
ETOOSINDIA.COM
5.
The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm
from the centre is 54 T. What will be its value at the centre of the loop ?
[AIEEE 4/300 2004]
(1) 250 T
(2) 150 T
(3) 125 T
(4) 75 T
6.
Two long conductors, separated by a distance d carry currents I1 and I2 in the same direction. They exert a force
F on each other. Now the current in one of them is increased to two times and its direction is reversed. The
distance is also increased to 3d. The new value of the force between them is :
[AIEEE 4/300 2004]
(1) 2 F
(2) F/3
(3) 2F/3
(4) F/3
7.
The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a
vibration magnetometer is 2s. The magnet is cut along its length into three equal parts and three parts are
then placed on each other with their like poles together. The time period of this combination will be :
[AIEEE 4/300 2004]
(1) 2s
(2) 2/3 s
(3) 2 3 s
(4) 2 / 3 s
8.
9.
Two thin, long, parallel wires, separated by a distance d carry a current of i A in the same direction. They
will :
(1) attract each other with a force of
0 i2
( 2d)
0i 2
(2d2 )
0 i2
( 2d)
0i 2
(2d2 )
10.
Two concentric coils each of radius equal to 2 cm are placed at right angles to each other. 3 ampere and 4
ampere are the currents flowing in each coil respectively.
[AIEEE 4/300 2005]
The magnetic induction in weber/m2 at the centre of the coils will be (0 = 4p 107 Wb/A.m):
(0 = 4p 107 Wb/A.m):
(1) 12 105
(2) 105
(3) 5 105
(4) 7 105
11.
A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an
electron is projected along the direction of the fields with a certain velocity, then :
[AIEEE 4/300 2005]
(1) its velocity will decrease
(2) its velocity will increase
(3) it will turn towards right of direction of motion (4) it will turn towards left of direction of motion.
12.
A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a
magnetic field B. The time taken by the particle to complete one revolution is :
[AIEEE 4/300 2005]
(1)
2mq
B
(2)
2q2B
B
(3)
2qB
m
(4)
2m
qB
13.
14.
In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other.
A charged particle is released from rest in this region. The path of the particle will be a : [AIEEE 1.5/180 2006]
(1) circle
(2) helix
(3) straight line
(4) ellipse
ETOOSINDIA.COM
15.
Needles N1, N2 and N3 are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will :
[AIEEE 1.5/180 2006]
(1) attract all three of them
(2) attract N1 and N2 strongly but repel N3
(3) attract N1 strongly, N2 weakly and repel N3 weakly
(4) attract N1 strongly, but repel N2 and N3 weakly
16.
A long solenoid has 200 turns per cm and carries a current i. The magnetic field at its centre is 6.28102
Weber/m2. Another long solenoid has 100 turns per cm and it carries a current i/3. The value of the magnetic
field at its centre is :
[AIEEE 4.5/180 2006]
(1) 1.05 104 Weber/m2
(2) 1.05 102 Weber/m2
(3) 1.05 105 Weber/m2
(4) 1.05 10103 Weber/m2
17.
A long straight wire of radius a carries a steady current i. The current is uniformly distributed across its
crosssection. The ratio of the magnetic field at
(1) 1/4
(2) 4
a
and 2a from axis is :
2
(3) 1
18.
A current I flows along the length of an infinitely long, straight, thin walled pipe. Then : [AIEEE 3/120 2007]
(1) the magnetic field is zero only on the axis of the pipe
(2) the magnetic field is different at different points inside the pipe
(3) the magnetic field at any point inside the pipe is zero
(4) the magnetic field at all points inside the pipe is the same, but not zero
19.
A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields E and
B with a velocity v perpendicular to both E and B , and comes out without any change in magnitude or
direction of v . Then :
[AIEEE 3/120 2007]
(1) v E B / B 2
(2) v E E / B 2
(3) v E E / E 2
(4) v B E / E 2
20.
A charged particle moves through a magnetic field perpendicular to its direction. Then : [AIEEE 3/120 2007]
(1) the momentum changes but the kinetic energy is constant
(2) both momentum and kinetic energy of the particle are not constant
(3) both, momentum and kinetic energy of the particle are constant
(4) kinetic energy changes but the momentum is constant
21.
Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an
electric current and COD carries a current . The magnetic field on a point lying at a distance d from O, in
a direction perpendicular to the plane of the wires AOB and COD, will be given by : [AIEEE 3/120 2007]
1/ 2
(1)
0 1 2
2 d
(2)
0 2
1 22
2d
1/ 2
(3)
0
( + )
2d 1 2
(4)
0 2
1 22
2d
22.
Relative permittivity and permeability of a material are r and r, respectively. Which of the following values of
these quantities are allowed for a diamagnetic material ?
[AIEEE 3/105 2008]
(1) r = 1.5 , r = 0.5
(2) r = 0.5 , r = 0.5
(3) r = 1.5 , r = 1.5
(4) r = 0.5 , r = 1.5
23.
A horizontal overhead powerline is at a height of 4 m from the ground and carries a current of 100 A from east
to west. The magnetic field directly below it on the ground is (0 = 4 107 T mA1):
[AIEEE 3/ 105 2008]
(1) 5 106 T northward
(2) 5 106 T southward
(3) 2.5 107 T northward
(4) 2.5 107 T southward
ETOOSINDIA.COM
Comprehension :
[AIEEE 2009 ]
24.
The magnitude of the magnetic field due to the loop ABCD at the origin (O) is:
(1)
25.
0 (b a )
24ab
0 b a
(2) 4 ab
0
(3) 4 2(b a) 3 (a b )
(4) zero
(2) The magnitude of the net force on the loop is given by 4 2(b a ) 3 (a b )
0 1
(b a).
24ab
27.
Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane
of the paper as shown. The variation of magnetic field B along the line XX is given by [AIEEE 4/144 2010]
(1)
(2)
(3)
(4)
A current I flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius R. The
magnitude of the the magnetic induction along its axis is :
[AIEEE 4/144 2011]
(A)
28.
0 I
2
(B)
0 I
22R
(C)
0 I
2 R
(D)
0 I
4R
Proton, Deutron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant
magnetic field. The radii of proton deuteron and alpha particle are respectively rp, rd, and r. Which of the
following relation is correct ?
[AIEEE 4/120 2012]
(1) r = rd > rp
(2) r = rp > rd
(3) r = rp < rd
(4) r > rd > rp
ETOOSINDIA.COM
NCERT QUESTIONS
1.
2.
3.
A short bar magnet placed with its axis at 30 with a uniform external magnetic field of 0.25 T experiences
a torque of magnitude equal to 4.5 x 10 2 J. What is the magnitude of magnetic moment of the magnet?
4.
A short bar magnet of magnetic moment m = 0.32 JT 1 is placed in a uniform external magnetic field of
0.15 T. If the bar is free to rotate in the plane of the field, which orientations would correspond to its (i)
stable and (ii) unstable equilibrium? What is the potential energy of the magnet in each case?
5.
A closely wound solenoid of 800 turns and area of cross-section 2.5 x 104 m 2 carries a current of 3.0
A Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic
moment ?
6.
A bar magnet of magnetic moment 1.5 JT 1 lies aligned with the direction of a uniform magnetic field of
0.22 T.
(a) What is the amount of work required by an external torque to turn the magnet so as to align its
magnetic moment, (i) normal to the field direction (ii) opposite to the field direction?
(b) What is the torque on the magnet in cases (i) and (ii)?
7.
A closely wound solenoid of 2000 turns and area of cross-section 1.6 x 104 m 2 , carrying a current of
4.0 A, is suspended through its centre allowing it to turn in a horizontal plane.
(a) What is the magnetic moment associated with the solenoid?
(b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5 x102 T is
set up at an angle of 30 with the axis of the solenoid ?
8.
At a certain location in Africa, a compass points 12 west of the geographic north. the north tip of the
magnetic needle of a dip circle placed in the plane of magnetic meridian points 60 above the horizontal.
The horizontal component of the earths field is measured to be 0.16 G. Specify the direction and
magnitude of the earths field at the location.
9.
A monoenergetic ( 18 keV ) electron beam initially in the horizontal direction is subject to a horizontal
magnetic field of 0.40 G. normal to the initial direction. Estimate the up or down deflection of the beam
over a distance of 30 cm,( m e= 9.11 x 1031 kg, e = 1.60 x 1019 C ).
[Note : Data in this exercise are so chosen that the answer will give you an idea of the effect of earths
magnetic field on the motion of the electron beam from the electron gun to the screen in a TV set]
ETOOSINDIA.COM
Exercise # 1
PART-I
A-1.*
(ABC) A-2.
(B)
A-3.
(A)
B-1.
(A)
B-2.
(B)
B-3.
(C)
C-1.
(A)
C-2.
(B)
C-3.
(D)
C-4.
(C)
C-5.
(A)
C-6.
(D)
C-7.
(B)
D-1.
(B)
D-2.
(D)
D-3.
(C)
D-4.
(B)
D-5.
(C)
D-6.
(B)
D-7.*
(AC)
D 8.*
(CD)
E-1.
(D)
E-2.*
(AD)
E-3.*
(BD)
E 4*.
(BD)
E-5.*
(AB)
F-1.
(C)
F-2.
(C)
F-3.
(B)
F-4.
(B)
F-5.
(D)
G-1.
(B)
G-2.
(A)
H-1.
(C)
H-2.
(A)
-1.
(C)
PART-II
1.
(C)
2.
(A)
3.
(A)
4.
5.
6.
Exercise # 2
PART-I
1.
(C)
2.
(C)
3.
(A)
4.
(A)
5.
(D)
6.
(C)
7.
(A)
8.
(D)
9.
(B)
10.
(A)
11.
(D)
12.
(C)
13.
(C)
14.*
(CD)
15.*
(AD)
16.*
(BCD) 17.*
(BCD) 18.*
(ABD) 19.*
(ABC)
PART-II
1..
13
10 -4 wb/m2
2
4
1013 (2 j + k ) (v) yes, no
27
2.
3.
(i)
4.
5.
4 10-5 wb/m2
6.
7.
8.
0i
,
4d
9.
0i
2x
10.
2 2 0i
a
11.
0 qv
4R
, inwards (ii)
0i
2 4d ,
(iv)
0 qv
4( x 2 R 2 )
, No
1
2
ETOOSINDIA.COM
12.
13.
8
5
T
(a) 5 10 1
13 13
14.
0 1
1
4 R1 R 2
15.
B=
16.
(a) B =
17.
(a) B 0 ( i 2k ) (b) B 0 i 1 1 k (c) B 0 j k
4 R
4R
4R
18.
B=
21.
2500 turns/m
25.
M3 L2 T 4 Q4
26.
(a) 4 A, (b)
(i) current directed into the plane of paper, 1 m from R on RQ (away from Q)
(ii) current directed out of from paper, 1 m from R on RQ (between R and Q)
27.
30
28.
41.
2 cm
42.
44.
(a)
8
x1012 m/s, No (b) 48 106 s
91
45.
(a)
mv
qB
46.
0i
2 22 21
4R
0 ni
2
19.
B=
22.
1V
0i
2b
20.
23.
12 cm 24.
D electron , B -particle
40.
20 cm,
8
182
x10 8 per sec
104 T,
4
91
43.
864
x1012 m/s2
5
47.
8 cm
48.
36 cm, 56 cm
49.
50.
16 106 m/s,
52.
53.
(a)
54.
50 m/s
59.
i
r 2ne
(b)
5
10 3 s 1
3.0
m
2qB
29.
20i
5r
mv 3 3m
,
qB 2
2qB
2qE 0 x
m
3
2
0 2
; (b) B = 0
4 2a
b (c) B = ( + tan ) 0 /2R = 28T..
4 a
b
(d)
57.
(b) zero
(c)
91
cm
20
51.
10 5 m/s, 2 10 5 m/s
(c) vB
(b)
iB
r2n
(c)
iB
r2ne
(d)
2iB
rne
55.
5
10 5 C/kg
4
58.
56.
5 10 3 N/C. 5 102 T
ETOOSINDIA.COM
60.
8 102 N
63.
64.
0 i1i2
r
n 2 = 40 n2 J/m
2
r1
65.
iB/2
66.
67.
0.12
68.
iB0
69.
70.
71.
40 cm
75 103 J
73.
(a) 2aiB, perpendicular to the plane of the figure going into it. (b)
1
T
2
102 N - m
78.
(a)
79.
80.
1
QR2
2
81.
V =
82.
3 31 10 -5 T, 30 E of N
83.
84.
6 104 T,
86.
3r
d=
88.
iL2B
4
61.
(b)
62.
2B 0 i
13
2 ai B 0
(b) 60
BiL2
18
278
139 3
kA
kA, H =
36
10 4 T
5
85.
105 T; 2 106 T
2 2 0i
a
0 j
87.
B=
89.
(a) Vmax =
2
qBd
2m
d
(b) 12 V
(c)
max
3d
mg
90.
i 1 2
91.
F=
n 1
i=
mg
= 2.5 A
2 BN
ETOOSINDIA.COM
Exercise # 3
PART-I
1.
(A)
2.
5.
(i) K = NAB
8.
(D)
3.
RP : R = 1 :
2 4.
NABQ
2 NAB 0
(iii)
(B)
6.*
(AC)
9.
(ACD)
10.
11.
12.
(C)
13.*
(BD)
15.*
18.
(D)
19.
(AC)
(ii)
14.
20.
(A)
7.
(A)
(CD)
16.
17.
(B)
(AD)
PART-II
1.
(1)
2.
(4)
3.
(2)
4.
(2)
5.
(1)
6.
(3)
7.
(2)
8.
(3)
9.
(1)
10.
(3)
11.
(1)
12.
(4)
13.
(3)
14.
(3)
15.
(3)
16.
(2)
17.
(3)
18.
(3)
19.
(1)
20.
(1)
21.
(2)
22.
(1)
23.
(2)
24.
(1)
25.
(1)
26.
(1)
27.
(1)
28.
(2)
Exercise # 4
1.
(a) In either case, one gets two magnets, each with a north and south pole,
(b) Molten iron is above the Curie temperature (770 C) and is, therefore, not ferromagnetic. An iron bar
magnet when melted does not does not retain its magnetism.
(c) No force if the field is uniform. The iron nail experiences a non-uniform magnetic field due to the bar
magnet. The induced magnetic moment in the nail, experiences both force and torque. The net force is
attractive because the induced (say) south pole in the nail is closer to the north pole of the magnet than the
induced north pole.
(d) Not necessarily. True only if the source of the field has a net non-zero magnetic moment. This is not so
for a toroid of even for a straight infinite conductor.
(e) Depends on what one means by three poles. Poles must always occur in pairs. But one can think to two
bar magnets with (say) their north ends glued together as providing a three-pole field configuration.
(f) Try to bring different ends of the magnets closer. A repulsive force in some situation establishes that both
are magnetized. If it is always attractive, then one of them is not magnetized. To see which one, pick up one,
say , A and lower one of the middle of B is magnetized. If you do not notice any change from the end to the
middle of B, then A is magnetized.
2.
(a) Magnetic declination, angle of dip, horizontal component of earths magnetic field.
(b) Greater in Britain (it is about 70) , because Britain is closer to the magnetic north pole.
(c) Field lines of B due to the earths magnetism would seen to come out of the ground.
3.
0.36 JT1
ETOOSINDIA.COM
4.
5.
0.60 JT 1 along the axis of the solenoid ; the direction determined by the sense of flow of current.
6.
7.
(a) 1.28 A m 2 along the axis in the direction related to the sense of current via the right-handed screw
rule.
(b) force is zero in uniform field; torque= 0.048 Nm in a direction that tends to align the axis of the
solenoid ( i.e., its magnetic moment vector) along. B.
8.
The earths field lines in a vertical 12 west of the geographic meridian making an angle of 60 (
upwards ) with the horizontal (magnetic south to magnetic north) direction. Magnitude = 0.32 G.
9.
R=
meV
eB
2m e x kinetic energy
eB
= 11.3 m
ETOOSINDIA.COM