Page 1
Introductory Exercise 24.1
Ques 1: Figure shows a conducting loop placed near a long straight
wire carrying a current i as shown. If the current increases
continuously, find the direction of the induced current in the loop.
Sol: magnetic field passing through loop is increasing. Hence induced current
will produce magnetic field. So, induced current should be anti-clockwise.
Ques 2: A metallic loop is placed in a nonuniform steady magnetic
field. Will an emf be induced in the loop?
Sol: It is true that magnetic flux passing through the loop is calculated by
integration. But it remains constant.
Ques 3: Write the dimensions of
Sol: = [Potential or EMF]
= [ML2A-1T-3]
Introductory Exercise 24.2
Ques 1: A triangular loop is placed in a dot magnetic field as
shown in figure. Find the direction of induced current in the loop if
magnetic field is increasing.
Page 2
Introductory Exercise 24.1
Ques 1: Figure shows a conducting loop placed near a long straight
wire carrying a current i as shown. If the current increases
continuously, find the direction of the induced current in the loop.
Sol: magnetic field passing through loop is increasing. Hence induced current
will produce magnetic field. So, induced current should be anti-clockwise.
Ques 2: A metallic loop is placed in a nonuniform steady magnetic
field. Will an emf be induced in the loop?
Sol: It is true that magnetic flux passing through the loop is calculated by
integration. But it remains constant.
Ques 3: Write the dimensions of
Sol: = [Potential or EMF]
= [ML2A-1T-3]
Introductory Exercise 24.2
Ques 1: A triangular loop is placed in a dot magnetic field as
shown in figure. Find the direction of induced current in the loop if
magnetic field is increasing.
Sol: is increasing. Hence is produced by the induced current. So, it is
clockwise.
Ques 2: A rectangular loop is placed near a current carrying straight
wire as shown in figure. If the loop is rotated about an axis passing
through one of its sides, find the direction of induced current in the
loop.
Sol: Magnetic lines around the straight wire are circular. So, same magnetic
lines will pass through loop under all conditions.
?F = 0 ? emf = 0 ? i = 0
Ques 3: Two circular loops lie side by side in the same plane. One is
connected to a source that supplies an increasing current, the other
is a simple closed ring. Is the induced current in the ring is in the
same direction as that in the loop connected to the source or
opposite? What if the current in the first loop is decreasing?
Sol: By increasing the current in loop-1 magnetic field in ring-2 in downward
direct ion will increase. Hence induced current in ring-2 should produce
upward magnetic field. Or current in ring should be in the same direction.
Introductory Exercise 24.3
Page 3
Introductory Exercise 24.1
Ques 1: Figure shows a conducting loop placed near a long straight
wire carrying a current i as shown. If the current increases
continuously, find the direction of the induced current in the loop.
Sol: magnetic field passing through loop is increasing. Hence induced current
will produce magnetic field. So, induced current should be anti-clockwise.
Ques 2: A metallic loop is placed in a nonuniform steady magnetic
field. Will an emf be induced in the loop?
Sol: It is true that magnetic flux passing through the loop is calculated by
integration. But it remains constant.
Ques 3: Write the dimensions of
Sol: = [Potential or EMF]
= [ML2A-1T-3]
Introductory Exercise 24.2
Ques 1: A triangular loop is placed in a dot magnetic field as
shown in figure. Find the direction of induced current in the loop if
magnetic field is increasing.
Sol: is increasing. Hence is produced by the induced current. So, it is
clockwise.
Ques 2: A rectangular loop is placed near a current carrying straight
wire as shown in figure. If the loop is rotated about an axis passing
through one of its sides, find the direction of induced current in the
loop.
Sol: Magnetic lines around the straight wire are circular. So, same magnetic
lines will pass through loop under all conditions.
?F = 0 ? emf = 0 ? i = 0
Ques 3: Two circular loops lie side by side in the same plane. One is
connected to a source that supplies an increasing current, the other
is a simple closed ring. Is the induced current in the ring is in the
same direction as that in the loop connected to the source or
opposite? What if the current in the first loop is decreasing?
Sol: By increasing the current in loop-1 magnetic field in ring-2 in downward
direct ion will increase. Hence induced current in ring-2 should produce
upward magnetic field. Or current in ring should be in the same direction.
Introductory Exercise 24.3
Ques 1: A loop of wire enclosing an area S is placed in a region where
the magnetic field is perpendicular to the plane. The magnetic
field varies wit h time according to the expression B = B0e-
at where a is so me constant. That is, at t = 0. The field is B0 and for t
> 0, the field decreases exponentially. Find the induced emf in the
loop as a function of time.
Sol:
Ques 2: As the bar shown in figure moves in a direct ion
perpendicular to the field, is an external force required to keep it
moving with constant speed.
Sol: Circuit is not closed. So, current is zero or magnetic force is zero.
Ques 3: A coil formed by wrapping 50 turns of wire in the shape of a
square is positioned in a magnetic field so that the normal to the
plane of the coil makes an angle of 30°, with the direction of the field.
When the magnetic field is increased uniformly from 200 µT to 600 µT
in 0.4 s, an emf of magnitude 80.0 mV is induced in the coil. What is
the total length of the wire?
Sol:
Page 4
Introductory Exercise 24.1
Ques 1: Figure shows a conducting loop placed near a long straight
wire carrying a current i as shown. If the current increases
continuously, find the direction of the induced current in the loop.
Sol: magnetic field passing through loop is increasing. Hence induced current
will produce magnetic field. So, induced current should be anti-clockwise.
Ques 2: A metallic loop is placed in a nonuniform steady magnetic
field. Will an emf be induced in the loop?
Sol: It is true that magnetic flux passing through the loop is calculated by
integration. But it remains constant.
Ques 3: Write the dimensions of
Sol: = [Potential or EMF]
= [ML2A-1T-3]
Introductory Exercise 24.2
Ques 1: A triangular loop is placed in a dot magnetic field as
shown in figure. Find the direction of induced current in the loop if
magnetic field is increasing.
Sol: is increasing. Hence is produced by the induced current. So, it is
clockwise.
Ques 2: A rectangular loop is placed near a current carrying straight
wire as shown in figure. If the loop is rotated about an axis passing
through one of its sides, find the direction of induced current in the
loop.
Sol: Magnetic lines around the straight wire are circular. So, same magnetic
lines will pass through loop under all conditions.
?F = 0 ? emf = 0 ? i = 0
Ques 3: Two circular loops lie side by side in the same plane. One is
connected to a source that supplies an increasing current, the other
is a simple closed ring. Is the induced current in the ring is in the
same direction as that in the loop connected to the source or
opposite? What if the current in the first loop is decreasing?
Sol: By increasing the current in loop-1 magnetic field in ring-2 in downward
direct ion will increase. Hence induced current in ring-2 should produce
upward magnetic field. Or current in ring should be in the same direction.
Introductory Exercise 24.3
Ques 1: A loop of wire enclosing an area S is placed in a region where
the magnetic field is perpendicular to the plane. The magnetic
field varies wit h time according to the expression B = B0e-
at where a is so me constant. That is, at t = 0. The field is B0 and for t
> 0, the field decreases exponentially. Find the induced emf in the
loop as a function of time.
Sol:
Ques 2: As the bar shown in figure moves in a direct ion
perpendicular to the field, is an external force required to keep it
moving with constant speed.
Sol: Circuit is not closed. So, current is zero or magnetic force is zero.
Ques 3: A coil formed by wrapping 50 turns of wire in the shape of a
square is positioned in a magnetic field so that the normal to the
plane of the coil makes an angle of 30°, with the direction of the field.
When the magnetic field is increased uniformly from 200 µT to 600 µT
in 0.4 s, an emf of magnitude 80.0 mV is induced in the coil. What is
the total length of the wire?
Sol:
Side of square = 1.36 m Total length of wire = 50 (4 × 1.36) = 272 m
Ques 4: The long straight wire in figure (a) carries a constant current
i. A metal bar of length l is moving at constant velocity v as shown in
figure. Point a is a distance d from the wire.
(a) Calculate the emf induced in the bar.
(b) Which point a or b is at higher potential?
(c) If the bar is replaced by a rectangular wire loop of resistance R,
what is the magnitude of current induced in the loop?
Sol: (a) At a distance x from the wire magnet ic field over the wire ab is
(b) Magnetic field due to current i over the wire ab is inwards. Velocity of wire
ab is towards right. Applying right hand rule we can see that a point is at
higher potential.
(c) Net change in flux through the loop abcd is zero.
Hence induced emf is zero. So, induced current is zero.
Page 5
Introductory Exercise 24.1
Ques 1: Figure shows a conducting loop placed near a long straight
wire carrying a current i as shown. If the current increases
continuously, find the direction of the induced current in the loop.
Sol: magnetic field passing through loop is increasing. Hence induced current
will produce magnetic field. So, induced current should be anti-clockwise.
Ques 2: A metallic loop is placed in a nonuniform steady magnetic
field. Will an emf be induced in the loop?
Sol: It is true that magnetic flux passing through the loop is calculated by
integration. But it remains constant.
Ques 3: Write the dimensions of
Sol: = [Potential or EMF]
= [ML2A-1T-3]
Introductory Exercise 24.2
Ques 1: A triangular loop is placed in a dot magnetic field as
shown in figure. Find the direction of induced current in the loop if
magnetic field is increasing.
Sol: is increasing. Hence is produced by the induced current. So, it is
clockwise.
Ques 2: A rectangular loop is placed near a current carrying straight
wire as shown in figure. If the loop is rotated about an axis passing
through one of its sides, find the direction of induced current in the
loop.
Sol: Magnetic lines around the straight wire are circular. So, same magnetic
lines will pass through loop under all conditions.
?F = 0 ? emf = 0 ? i = 0
Ques 3: Two circular loops lie side by side in the same plane. One is
connected to a source that supplies an increasing current, the other
is a simple closed ring. Is the induced current in the ring is in the
same direction as that in the loop connected to the source or
opposite? What if the current in the first loop is decreasing?
Sol: By increasing the current in loop-1 magnetic field in ring-2 in downward
direct ion will increase. Hence induced current in ring-2 should produce
upward magnetic field. Or current in ring should be in the same direction.
Introductory Exercise 24.3
Ques 1: A loop of wire enclosing an area S is placed in a region where
the magnetic field is perpendicular to the plane. The magnetic
field varies wit h time according to the expression B = B0e-
at where a is so me constant. That is, at t = 0. The field is B0 and for t
> 0, the field decreases exponentially. Find the induced emf in the
loop as a function of time.
Sol:
Ques 2: As the bar shown in figure moves in a direct ion
perpendicular to the field, is an external force required to keep it
moving with constant speed.
Sol: Circuit is not closed. So, current is zero or magnetic force is zero.
Ques 3: A coil formed by wrapping 50 turns of wire in the shape of a
square is positioned in a magnetic field so that the normal to the
plane of the coil makes an angle of 30°, with the direction of the field.
When the magnetic field is increased uniformly from 200 µT to 600 µT
in 0.4 s, an emf of magnitude 80.0 mV is induced in the coil. What is
the total length of the wire?
Sol:
Side of square = 1.36 m Total length of wire = 50 (4 × 1.36) = 272 m
Ques 4: The long straight wire in figure (a) carries a constant current
i. A metal bar of length l is moving at constant velocity v as shown in
figure. Point a is a distance d from the wire.
(a) Calculate the emf induced in the bar.
(b) Which point a or b is at higher potential?
(c) If the bar is replaced by a rectangular wire loop of resistance R,
what is the magnitude of current induced in the loop?
Sol: (a) At a distance x from the wire magnet ic field over the wire ab is
(b) Magnetic field due to current i over the wire ab is inwards. Velocity of wire
ab is towards right. Applying right hand rule we can see that a point is at
higher potential.
(c) Net change in flux through the loop abcd is zero.
Hence induced emf is zero. So, induced current is zero.
Introductory Exercise 24.4
Q 1. The current through an inductor of 1H is given by, i = 3t sin t. Find the voltage across the inductor.
Solutions
1.
Here L = 1H and
di
dt
= 3 [sin t + t cos t]
|e| = 3(t cos t+ sin t)
Introductory Exercise 24.5
Q 1. (a) Calculate the self inductance of a solenoid that is tightly wound with wire of diameter 0.10 cm,
has a cross-sectional area 0.90 cm
2
and is 40 cm long.
(b) If the current through the solenoid decreases uniformly from 10 A to 0A in 0.10s, what is the
emf induced between the ends of the solenoid?
Q 2. An inductor is connected to a battery through a switch. The emf induced in the inductor is much
larger when the switch is opened as compared to the emf induced when the switch is closed. Is this
statement true or false?
Solutions
1. (a)
= 4.5 × 10
-5
H
(b)
= 4.5 × 10
-3
V
2. When switch is opened current suddenly decreasing from steady state value to zero. When switch
is closed it takes time to increase from 0 to steady state value.
?t in second case in large. Hence induced emf is less.
Introductory Exercise 24.6
Q 1. Two single turn circular loops of wire have radii R and r (R>>r). The loops lie in the same plane
and are concentric. Show that the mutual inductance of the pair is
2
0
r
2R
??
.
Solutions
1. Magnetic field due to large loop,
Area of smaller loop
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