UNIT III

MAGNETIC EFFECTS OF CURRENT AND

MAGNETISM

Weightage 8 Marks

Concept of magnetic field and Oersted’s experiment Biot-savart law and its
application to current carrying circular loop.
Ampere’s law and its applications to infinitely long straight wire, straight and
toroidal solenoids.
Force on a moving charge in uniform magnetic and electric fields.

Cyclotron
Force on a current carrying conductor in a uniform magnetic field, force
between two parallel current carrying conductors, definition of ampere. Torque
experienced by a current loop in a uniform magnetic field.
Moving coil Galvanometer – its current sensitivity.

Moving Coil Galvanometer – Conversion to ammeter and voltmeter, Current

loop as a magnetic dipole and it’s magnetic dipole moment, Magnetic dipole
moment of a revolving electron, Magnetic field intensity due to a magnetic
dipole (bar magnet) along it’s axis and perpendicular to it’s axis.

Torque on a magentic dipole (bar magnet) in a uniform magnetic field; bar

magnet as an equivalent solenoid, Magnetic field lines Earth’s Magnetic
field and magnetic elements. Para-, dia- and ferro-magnetic substances with
examples.
Electromagnets and factors affecting their strengths, Permanent magnets.

55 XII – Physics
 1. Must every magnetic field configuration have a north pole and a south
pole? What about the field due to a toroid?

2. How are the figure of merit and current sensitivity of galvanometer related
with each other?

3. Show graphically the variation of magnetic field due to a straight conductor

of uniform cross-section of radius ‘a’ and carrying steady currently as a
function of distance r (a > r) from the axis of the conductor.
4. The force per unit length between two parallel long current carrying
conductor is F. If the current in each conductor is tripled, what would be
the value of the force per unit length between them?
5. How does the angle of dip vary from equator to poles?
6. What is the effect on the current measuring range of a galvanometer when
it is shunted?
7. An electric current flows in a horizontal wire from East to West. What will
be the direction of magnetic field due to current at a point (i) North of wire;
(ii) above the wire.
8. Suggest a method to shield a certain region of space from magnetic fields.
*9. Why the core of moving coil galvanometer is made of soft iron?
10. Where on the earth’s surface, is the vertical component of earth’s magnetic
field zero?
11. If the current is increased by 1% in a moving coil galvanometer. What will
be percentage increase in deflection?
12. Write S.I. unit of (i) Pole strength and (ii) Magnetic dipole moment.

13. If the magnetic field is parallel to the positive y-axis and the charged
particle is moving along the positive x-axis, which way would the Lorentz
force be for (a) an electron (negative charge), (b) a proton (positive charge)

Sol : When velocity v of positively charged particle is along x-axis and
  
the magnetic field B is along y-axis, so v B is along the z-axis (Fleming’s
s
left hand rule).

63 XII – Physics
 Therefore,

(a) for electron Lorentz force will be along –z axis;

(b) for a positive charge (proton) the force is along +z axis.

14. If a toroid uses Bismuth as its core, will the field in the core be lesser or
greater than when it is empty?

Ans : Bismuth is diamagnetic, hence, the overall magnetic field will be

slightly less.

15. An electron beam projected along + x-axis, experiences a force due to a

magnetic field along the + y-axis. What is the direction of the magnetic
field?

Ans : +Z axis.

16. What is the principle of a moving coil galvanometer?

Ans : When a current carrying coil is placed in uniform magnetic field, it

experiences a torque.

17. What is the direction of magnetic dipole moment?

Ans : S to N

18. What is the angle of dip at a place where vertical and horizontal component
of earth’s field are equal?

Ans : 45°

19. Is any work done on a moving charge by a magnetic field?

Ans : No, as magnetic field is in perpeudicular direction.

20. Sketch the magnetic field lines for a current carrying circular loop.

Ans :

XII – Physics 64
1. Write the four measures that can be taken to increase the sensitivity of a
galvanometer.

2. A galvanometer of resistance 120 gives full scale deflection for a current

of 5mA. How can it be converted into an ammeter of range 0 to 5A? Also
determine the net resistance of the ammeter.

3. A current loop is placed in a uniform magnetic field in the following

orientations (1) and (2). Calculate the magnetic moment in each case.

n B
(1) (2) B

n
4. A current of 10A flows through a semicircular wire of radius 2cm as shown
in figure (a). What is direction and magnitude of the magnetic field at the
centre of semicircle? Would your answer change if the wire were bent as
shown in figure (b)?

2cm 2cm
10A
10A
Fig. (a) Fig. (b)
5. A proton and an alpha particle of the same enter, in turn, a region of
uniform magnetic field acting perpendicular to their direction of motion.
Deduce the ratio of the radii of the circular paths described by the proton
and alpha particle.
6. Which one of the two an ammeter or milliammeter, has a higher resistance
and why?

7. Mention two properties of soft iron due to which it is preferred for making
electromagnet.
8. A magnetic dipole of magnetic moment M is kept in a magnetic field B.
What is the minimum and maximum potential energy? Also give the most
stable position and most unstable position of magnetic dipole.

65 XII – Physics
 9. What will be (i) Pole strength (ii) Magnetic moment of each of new piece
of bar magnet if the magnet is cut into two equal pieces :
(a) normal to its length?

(b) along its length?

10. A steady current I flows along an infinitely long straight wire with circular
cross-section of radius R. What will be the magnetic field outside and
inside the wire at a point r distance far from the axis of wire?

11. A circular coil of n turns and radius R carries a current I. It is unwound and
rewound to make another square coil of side ‘a’ keeping number of turns
and current same. Calculate the ratio of magnetic moment of the new coil
and the original coil.

12. A coil of N turns and radius R carries a current I. It is unwound and

rewound to make another coil of radius R/2, current remaining the same.
Calculate the ratio of the magnetic moment of the new coil and original
coil.
13. At a place horizontal component of the earths magnetic field is B and
angle of dip at the place is 60°. What is the value of horizontal component
of the earths magnetic field.
(i) at Equator; (ii) at a place where dip angle is 30°
14. A galvanometer coil has a resistance G. 1% of the total current goes
through the coil and rest through the shunt. What is the resistance of the
shunt?
15. Prove that the magnetic moment of a hydrogen atom in its ground state
is eh/4 m. Symbols have their usual meaning.
16. Each of eight conductors in figure carries 2A of current into or out of page.

Two path are indicated for the line integral  B . d l. What is the value
of the integral for the path (a) and (b).

× ×

×
×

(a) (b)

XII – Physics 66
17. What is the radius of the path of an electron (mass 9 x 10 –31 kg and
charge 1.6 x 10 –19 C) moving at a speed of 3 x 10 7 m/s in a magnetic field
of 6 x 10–4 T perpendicular to it? What is its frequency? Calculate its
energy in keV. (1 eV = 1.6 x 10–19 J).

Sol : Radius, r = mv/ (qB)

= 9.1 x 10–31kg x 3 x 107 ms–1/ (1.6 x 10–19 C x 10–4 T) = 26 cm

= v/(2 r) = 2 x 108 s–1 = 2 x 108 Hz = 200 MHz.

E = (½)mv2 = (½) 9 x 10–31 kg x 9 x 1014 m2/s2

= 40.5 x 10–17 J = 4 x 10–16 J = 2.5 keV.

18. A particle of mass m and charge q moves at right angles to a uniform

magnetic field. Plot a graph showing the variation of the radius of the
circular path described by it with the increase in its kinetic energy, where,
other factors remain constant.

Ans : r K.E
Radius

Kinetic Energy
19. Magnetic field arises due to charges in motion. Can a system have magnetic
moments even though its net charges is zero? Justify.

Ans : Yes; for example the atoms of a paramagnetic substance possess

a net magnetic moment though its net charge is zero.

20. Define the term magnetic dipole moment of a current loop. Write the
expression for the magnetic moment when an electron revolves at a speed
‘v’, around an orbit of radius ‘r’ in hydrogen atom.

Ans : The product of the current in the loop to the area of the loop is
the magnetic dipole moment of a current loop.
The magnetic moment of electron
e   e   e 
– r v – r p – 
2 2me 2me

67 XII – Physics
 1. Derive the expression for force between two infinitely long parallel straight
wires carrying current in the same direction. Hence define ‘ampere’ on the
basis of above derivation.

2. Define (i) Hysteresis (ii) Retentivity (iii) Coercivity

3. Distinguish between diamagnetic, paramagnetic and ferromagnetic

substances in terms of susceptibility and relative permeability.

*4. Name all the three elements of earth magnetic field and define them with
the help of relevant diagram.

5. Describe the path of a charged particle moving in a uniform magnetic field

with initial velocity

(i) parallel to (or along) the field.

(ii) perpendicular to the field.

(iii) at an arbitrary angle (0° < < 90°).

6. Obtain an expression for the magnetic moment of an electron moving with

a speed ‘v’ in a circular orbit of radius ‘r’. How does this magnetic moment
change when :

(i) the frequency of revolution is doubled?

(ii) the orbital radius is halved?

7. State Ampere, circuital law. Use this law to obtain an expression for the
magnetic field due to a toroid.

*8. Obtain an expression for magnetic field due to a long solenoid at a point
inside the solenoid and on the axis of solenoid.

9. Derive an expression for the torque on a magnetic dipole placed in a

magnetic field and hence define magnetic moment.

10. Derive an expression for magnetic field intensity due to a bar magnet
(magnetic dipole) at any point (i) Along its axis (ii) Perpendicular to the axis.

*11. Derive an expression for the torque acting on a loop of N turns of area A
of each turn carrying current I, when held in a uniform magnetic field B.

XII – Physics 68
*12. How can a moving coil galvanometer be converted into a voltmeter of a
given range. Write the necessary mathematical steps to obtain the value
of resistance required for this purpose.

13. A long wire is first bent into a circular coil of one turn and then into a
circular coil of smaller radius having n turns. If the same current passes
in both the cases, find the ratio of the magnetic fields produced at the
centres in the two cases.

Ans : When there is only one turn, the magnetic field at the centre,
µ0 I
B
2a
1
2 a xn = 2 a a1 = a/n

µ0nI µ0n2 I
The magnetic field at its centre, B1 n2B
2a n 2a
The ratio is, B1/B = n2

1. How will a diamagnetic, paramagnetic and a ferromagnetic material behave

when kept in a non-uniform external magnetic field? Give two examples of
each of these materials. Name two main characteristics of a ferromagnetic
material which help us to decide suitability for making
(i) Permanent magnet (ii) Electromagnet.

2. State Biot-Savart law. Use it to obtain the magnetic field at an axial point,
distance d from the centre of a circular coil of radius ‘a’ and carrying
current I. Also compare the magnitudes of the magnetic field of this coil
at its centre and at an axial point for which the value of d is 3a.

3. Write an expression for the force experienced by a charged particle moving

in a uniform magnetic field B. With the help of diagram, explain the principle
and working of a cyclotron. Show that cyclotron frequency does not depend
on the speed of the particle.

*4. Write the principle, working of moving coil galvanometer with the help of
neat labelled diagram. What is the importance of radial field and phosphor
bronze used in the construction of moving coil galvanometer?

69 XII – Physics
 1. An electron travels on a circular path of radius 10m in a magnetic field of
2 × 10–3 T. Calculate the speed of electron. What is the potential difference
through which it must be accelerated to acquire this speed? [Ans. :
Speed = 3.56 × 109 m/s; V = 3.56 × 107 volts]

2. A ship is to reach a place 15° south of west. In what direction should it

be steered if declination at the place is 18° west? [Ans. : 87° west of
North]

3. Calculate the magnetic field due to a circular coil of 500 turns and of mean
diameter 0.1m, carrying a current of 14A (i) at a point on the axis distance
0.12m from the centre of the coil (ii) at the centre of the coil. [Ans. : (i)
5.0 × 10–3 Tesla; (ii) 8.8 × 10–2 tesla]

4. An electron of kinetic energy 10 keV moves perpendicular to the direction

of a uniform magnetic field of 0.8 milli testa. Calculate the time period of
rotation of the electron in the magnetic field.
[Ans. : 4.467 × 10 –8 s.]

5. If the current sensitivity of a moving coil galvanometer is increased by 20%

and its resistance also increased by 50% then how will the voltage sensitivity
of the galvanometer be affected?
[Ans. : 25% decrease]

6. A uniform wire is bent into one turn circular loop and same wire is again
bent in two turn circular loop. For the same current passed in both the
cases compare the magnetic field induction at their centres.
[Ans. : Increased 4 times]

7. A horizontal electrical power line carries a current of 90A from east to west
direction. What is the magnitude and direction of magnetic field produced
by the power line at a point 1.5m below it?
[Ans. : 1.2 × 10–5 T south ward]

*8. A galvanometer with a coil of resistance 90 shows full scale deflection

for a potential difference 225 mV. What should be the value of resistance
to convert the galvanometer into a voltmeter of range 0V to 5V. How
should it be connected? [Ans. : 1910 in series]

9. Two identical circular loops P and Q carrying equal currents are placed
such that their geometrical axis are perpendicular to each other as shown
in figure. And the direction of current appear’s anticlockwise as seen from

XII – Physics 70
 point O which is equidistant from loop P and Q. Find the magnitude and
direction of the net magnetic field produced at the point O.

I
O
R

P x
x

Q R
I
2
µ 0IR 2
Ans. :
2 2 32
2 R x
10. A cyclotron’s oscillator frequency is 10 MHz. What should be the operating
magnetic field for accelerating protons, if the radius of its dees is 60cm?
What is the kinetic energy of the proton beam produced by the accelerator?
Given e = 1.6 × 10–19 C, m = 1.67 × 10–27 kg. Express your answer in units
of MeV [1MeV = 1.6 × 10–13 J]. [Ans. : B = 0.656T, Emax = 7.421 MeV]
11. The coil of a galvanometer is 0.02 × 0.08 m2. It consists of 200 turns of
fine wire and is in a magnetic field of 0.2 tesla. The restoring forque
constant of the suspension fibre is 10 –6 Nm per degree. Assuming the
magnetic field to be radial.
(i) what is the maximum current that can be measured by the
galvanometer, if the scale can accommodate 30° deflection?
(ii) what is the smallest, current that can be detected if the minimum
observable deflection is 0.1°?
[Ans. : (i) 4.69 × 10–4 A; (ii) 1.56 × 10–6 A]
12. A voltmeter reads 8V at full scale deflection and is graded according to its
resistance per volt at full scale deflection as 5000 V–1. How will you
convert it into a voltmeter that reads 20V at full scale deflection? Will it still
be graded as 5000 V–1? Will you prefer this voltmeter to one that is
graded as 2000 V–1? [Ans. : 7.5 × 104 ]

13. A short bar magnet placed with its axis at 30° with an external field 1000G
experiences a torque of 0.02 Nm. (i) What is the magnetic moment of the

71 XII – Physics
 magnet. (ii) What is the work done in turning it from its most stable
equilibrium to most unstable equilibrium position?
[Ans. : (i) 0.4 Am2; (ii) 0.08 J]

14. What is the magnitude of the equatorial and axial fields due to a bar
magnet of length 4cm at a distance of 40 cm from its mid point? The
magnetic moment of the bar magnet is 0.5 Am2.
[Ans. : BE = 7.8125 × 10–7 T; BA = 15.625 × 10–7 T]

15. What is the magnitude of magnetic force per unit length on a wire carrying
a current of 8A and making an angle of 30° with the direction of a uniform
magnetic field of 0.15T?

16. Two moving coil galvanometers, M1 and M2 have the following

specifications.

R1 = 10 , N1 = 30, A1 = 3.6 x 10–3m2, B1 = 0.25T

R2 = 14 , N2 = 42, A2 = 1.8 x 10–3m2, B2 = 0.50T

Given that the spring constants are the same for the two galvano meters,
determine the ratio of (a) current sensitivity (b) voltage sensitivity of M 1 &
M2.

17. In the given diagram, a small magnetised needle is placed at a point O.

The arrow shows the direction of its magnetic moment. The other arrows
shown different positions and orientations of the magnetic moment of
another identical magnetic needs B

B4

B5 C A B3
B2

B6
(a) In which configuration is the systems not in equilibrium?

(b) In which configuration is the system.

(i) stable and (ii) unstable equilibrium?

XII – Physics 72
 (c) Which configuration corresponds to the lowest potential energy
among all the configurations shown?

18. In the circuit, the current is to be measured. What is the value of the
current if the ammeter shown :

3
3V

(a) is a galvanometer with a resistance RG = 60 ,

(b) is a galvanometer described in (i) but converted to an ammeter by

a shunt resistance r s = 0.02

(c) is an ideal ammeter with zero resistance?

19. An element l x i is placed at the origin and carries a large current

I = 10A. What is the magnetic field on the y-axis at a distance of 0.5m.
x = 1 cm.
y

0.5

x x
20. A straight wire of mass 200g and length 1.5 m carries a current of 2A. It
s suspended in mid-air by a uniform horizontal magnetic field B. What is
the magnitude of the magnetic field?

21. A rectangular loop of sides 25 cm and 10 cm carrying current of 15A is

placed with its longer side parallel to a long straight conductor 2.0 cm
apart carrying a current of 25A. What is the new force on the loop?
Ans : 7.82 x 10–4 N towards the conductor

Hint :

2I1I2 10 –7 2 25 15 0.25
F1 0
 9.38 10 –4 N attractive
4 r1 0.02

73 XII – Physics
 2I12
I 10 –7 2 25 15 0.25
F2 0
 1.56 10 –4 Nrepalsive
4 r2 0.12

Net F = F1 – F2 = 7.82 x 10–4 N

15A

25A 25 cm

2
cm 10 cm

22. In a chamber of a uniform magnetic field 6.5G is maintained. An electron

is shot into the field with a speed of 4.8 x 10 6 ms–1 normal to the field.
Explain why the path of electron is a circle.

(a) Determine the radius of the circular orbit (e = 1.6 x 10 –19 C, me =

9.1 x 10–31 kg)

(b) Obtain the frequency of resolution of the electron in its circular

orbit.

me 9.1 10 –31 4.8 106

Hint : (a) r 4.2 cm
eB 1.6 10 –19 6.5 10 –4

1 eB 1.6 10 –19 6.510 –4

(b) frequency 1.8 MH2
T 2 me 2 3.14 9.1 10 –31

1. The figure shows four directions of motion of a positively charged particle

moving through a uniform electric field E (directed out of the page and
represented with an encircled dot) and a uniform magnetic field B . (a)
Rank, directions 1, 2 and 3 according to the magnitude of the net force on
the particle, maximum first. (b) Of all four directions, which might result in
a net force of zero?

XII – Physics 74
 1
B
V1
V4
3 2
V2
V3
E
4

V1 = V2 = V3 = V 4

2. The true value of dip at a place is 30°. The vertical plane carrying the
needle is turned through 45° from the magnetic meridian. Calculate the
apparent value of dip. [Ans. : ´ = 39°14´]
3. Figure shows the path of an electron that passes through two regions
containing uniform magnetic fields of magnitude B1 and B2. Its path in each
region is a half circle. (a) Which field is stronger? (b) What are the directions
of two fields? (c) Is the time spend by the electron in the B1 , region greater
than, less than, or the same as the time spent in B2 region?

[Ans. : (a) B1 > B2; (b) B1 inward; B2 outward. (c) Time spent in B1 <
Time spent in B2]

B1

B2

75 XII – Physics
 1. No, pole exists only when the source has some net magnetic moment. In
toroid, there is no pole.

1. The figure shows two wires 1 and 2 both carrying the same current I from
point a to point b through the same uniform magnetic field B. Determine
the force acting on each wire.

Ans. : Same for both = ILB

× × × × × × × × × ×
× × 1 × × × 2 × ×
× × × × × × × ×
× × × × × × × × ×
a × × L× × ×b a × × L× × ×b
2. Reciprocal. 3. Fig. NCERT.

4. Nine Times. 5. 0° to 90°

6. Increased.

7. (i) Going into the plane of the paper; (ii) Emerging out of the plane of the
paper.

8. By putting in a ferromagnetic case

10. At equator. 11. 1%.

12. (i) Am; (ii) Am2.

3
Ig 5 10
2. S G 3
120 0.12 .
I Ig 5 5 10

3. (i) – mB (ii) zero

XII – Physics 76
 –7
10 10 5
4. (i) B 2
5 10 T outwards .
2 10
(ii) B = 5p × 10–5 T (inwards).

m 4m rp 1
5. rp and r 2r .
qB 2q B ra 2
6. RmA > RA.

7. Low Retentivity and high permeability.

8. Minimum potential = – MB when = 0 (most stable position)

Maximum potential = MB when = 180° (most unstable position).

9. (a) Pole strength same; magnetic moment half.

(b) pole strength half; magnetic moment half.

R R

r r

I 2
10. B 2 r µ0 2
r
R
µ0 I
B 2
r R r
2 R

 B . d l. = µ0 I

µ0 I
B r R .
2 r

11. M1 MI R2 ; M2 MIa2

R
2 rN 4aN a
2

77 XII – Physics
 M2
4
M1
2
r
2I
mnew 2 1
12. 2
.
moriginal I R 2

13. 0° and 90°.

 
14. (a)  B.dl 0I 2 0 Tm

(b) zero

15. Force experienced by current carrying conductor in magnetic field.

 
F IL B ILBsin
F
Hence, force permit length, f IB sin 30
L

= 8 x 0.15 x ½ = 0.6 Nm–1

NBA
16. (a) Current sensitivity,
I K
N1 B1 A1 N2 B2 A 2
Ratio of current Sensitivity =
K K
30 0.25 3.6 10 –3
57
42 0.50 1.8 10 –3

NBA
(b) Voltage sensitivity,
V kR

N1 B1 A1 N2B2 A 2
Ratio of voltage sensitivity
kR1 kR2

30 0.25 3.6 10–3 14

1
42 0.50 1.8 10–3 10

XII – Physics 78
17. (a) For equilibrium, the dipole moment should be parallel or auto parallel
to B. Hence, AB1 and AB2 are not in equilibrium.

(b) (i) for stable equilibrium, the dipole moments should be parallel,
examples : AB5 and AB6 (ii) for unstable equilibrium, the dipole
moment should be anti parallel examples : AB3 and AB4

(c) Potential energy is minimum when angle between M and B is 0°,

i.e, U = –MB Example : AB6

18. (a) Total resistance, RG + 3 = 63 .

3V
Hence, I 0.048A
63

(b) Resistance of the galvanometer as ammeter is

RGrS 60 0.02
0.02 .
RGrS 60 0.02

Total resistance R = 0.02 + 3 = 3.02

3
Hence, I 0.99A
302

(c) For the ideal ammeter, resistance is zero, the current,

I = 3/3 = 1.00A


19. From Biot-Sayart’s Law, d Id sin / r 2

dl = x = 1 cm = 10–2m, I = 10A, r = y = 0.5m

o/4 = 10–7 Tm/A, = 90° so sin
 10–7 10 10–2
dB 4 10–8 T along z axis
25 10–2

20. Force experienced by wire Fm = BIl (due to map field)

The force due to gravity, Fg = mg

0.2 9.8
mg = BIl B = mg/Il 0.657 T
2 1.5

[Earth’s magigield 4 x 10–5 T is negligible]

79 XII – Physics