# Electromagnetic Induction: JEE Advance (Part - 1) - Physics, Solution by DC Pandey Notes | Study DC Pandey Solutions for JEE Physics - JEE

## JEE: Electromagnetic Induction: JEE Advance (Part - 1) - Physics, Solution by DC Pandey Notes | Study DC Pandey Solutions for JEE Physics - JEE

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``` Page 1

Objective Questions
Single Correct Option
Q 1.  Two ends of an inductor of inductance L are connected to two parallel conducting wires. A rod of
length l and mass m is given velocity v
0
as shown. The whole system is placed in perpendicular
magnetic field B. Find the maximum current in the inductor, (neglect gravity and friction)

(a)
0
mv
L
(b)
0
m
v
L
(c)
2
0
mv
L
(d) None of these
Q 2.  A conducting rod is moving with a constant velocity v over the parallel conducting rails which are
connected at the ends through a resistor R and capacitor C as shown in the figure. Magnetic field
B is into the plane. Consider the following statements

(i) Current in loop AEFBA is anticlockwise (ii) Current in loop AEFBA is clockwise (iii) Current
through the capacitor is zero (iv) Energy stored in the capacitor is
2 2 2
1
CB L v
2

Which of the following options is correct?
(a) Statements (i) and (iii) are correct  (b) Statements (ii) and (iv) are correct
(c) Statements (i), (iii) and (iv) are correct  (d) None of these
Q 3.  A rod is rotating with a constant angular velocity ? about point O (its centre) in a magnetic field B
as shown. Which of the following figure correctly shows the distribution of charge inside the rod?

(a)    (b)    (c)    (d)
Q 4.  A straight conducting rod PQ is executing SHM in xy plane from x = - d to x = + d. Its mean
position is x = 0 and its length is along y-axis. There exists a uniform magnetic field B from x = -
Page 2

Objective Questions
Single Correct Option
Q 1.  Two ends of an inductor of inductance L are connected to two parallel conducting wires. A rod of
length l and mass m is given velocity v
0
as shown. The whole system is placed in perpendicular
magnetic field B. Find the maximum current in the inductor, (neglect gravity and friction)

(a)
0
mv
L
(b)
0
m
v
L
(c)
2
0
mv
L
(d) None of these
Q 2.  A conducting rod is moving with a constant velocity v over the parallel conducting rails which are
connected at the ends through a resistor R and capacitor C as shown in the figure. Magnetic field
B is into the plane. Consider the following statements

(i) Current in loop AEFBA is anticlockwise (ii) Current in loop AEFBA is clockwise (iii) Current
through the capacitor is zero (iv) Energy stored in the capacitor is
2 2 2
1
CB L v
2

Which of the following options is correct?
(a) Statements (i) and (iii) are correct  (b) Statements (ii) and (iv) are correct
(c) Statements (i), (iii) and (iv) are correct  (d) None of these
Q 3.  A rod is rotating with a constant angular velocity ? about point O (its centre) in a magnetic field B
as shown. Which of the following figure correctly shows the distribution of charge inside the rod?

(a)    (b)    (c)    (d)
Q 4.  A straight conducting rod PQ is executing SHM in xy plane from x = - d to x = + d. Its mean
position is x = 0 and its length is along y-axis. There exists a uniform magnetic field B from x = -
d to x = 0 pointing inward normal to the paper and from x = 0 to = + d there exists another
uniform magnetic field of same magnitude B but pointing outward normal to the plane of the
paper. At the instant t = 0, the rod is at x ~ 0 and moving to the right. The induced emf ( ?)

across
the rod PQ vs time (t) graph will be

(a)      (b)
(c)      (d)
Q 5.  Two parallel long straight conductors lie on a smooth plane surface. Two other parallel conductors
rest on them at right angles so as to form a square of side a. A uniform magnetic field B exists at
right angles to the plane containing the conductors. Now conductors start moving outward with a
constant velocity v
0
at t = 0. Then induced current in the loop at any time t is ( ? is resistance per
unit length of the conductors)

(a)
0
0
aBv
(a v t) ??
(b)
0
aBv
2 ?
(c)
0
Bv
?
(d)
0
Bv
2 ?

Q 6.  A conducting square loop is placed in a magnetic field B with its plane perpendicular to the field.
Some how the sides of the loop start shrinking at a constant rate ?. The induced emf in the loop at
an instant when

its side is a, is
(a) 2a ?B  (b) a
2
?B  (c) 2a
2
?B  (d) a ?B
Q 7.  A conducting straight wire PQ of length l is fixed along a diameter of a non-conducting ring as
shown in, the figure. The ring is given a pure rolling motion on a horizontal surface such that its
centre of mass has a velocity v. There exists a uniform horizontal magnetic field B in horizontal
direction perpendicular to the plane of ring. The magnitude of induced emf in the wire PQ at the
position shown in the figure will be
Page 3

Objective Questions
Single Correct Option
Q 1.  Two ends of an inductor of inductance L are connected to two parallel conducting wires. A rod of
length l and mass m is given velocity v
0
as shown. The whole system is placed in perpendicular
magnetic field B. Find the maximum current in the inductor, (neglect gravity and friction)

(a)
0
mv
L
(b)
0
m
v
L
(c)
2
0
mv
L
(d) None of these
Q 2.  A conducting rod is moving with a constant velocity v over the parallel conducting rails which are
connected at the ends through a resistor R and capacitor C as shown in the figure. Magnetic field
B is into the plane. Consider the following statements

(i) Current in loop AEFBA is anticlockwise (ii) Current in loop AEFBA is clockwise (iii) Current
through the capacitor is zero (iv) Energy stored in the capacitor is
2 2 2
1
CB L v
2

Which of the following options is correct?
(a) Statements (i) and (iii) are correct  (b) Statements (ii) and (iv) are correct
(c) Statements (i), (iii) and (iv) are correct  (d) None of these
Q 3.  A rod is rotating with a constant angular velocity ? about point O (its centre) in a magnetic field B
as shown. Which of the following figure correctly shows the distribution of charge inside the rod?

(a)    (b)    (c)    (d)
Q 4.  A straight conducting rod PQ is executing SHM in xy plane from x = - d to x = + d. Its mean
position is x = 0 and its length is along y-axis. There exists a uniform magnetic field B from x = -
d to x = 0 pointing inward normal to the paper and from x = 0 to = + d there exists another
uniform magnetic field of same magnitude B but pointing outward normal to the plane of the
paper. At the instant t = 0, the rod is at x ~ 0 and moving to the right. The induced emf ( ?)

across
the rod PQ vs time (t) graph will be

(a)      (b)
(c)      (d)
Q 5.  Two parallel long straight conductors lie on a smooth plane surface. Two other parallel conductors
rest on them at right angles so as to form a square of side a. A uniform magnetic field B exists at
right angles to the plane containing the conductors. Now conductors start moving outward with a
constant velocity v
0
at t = 0. Then induced current in the loop at any time t is ( ? is resistance per
unit length of the conductors)

(a)
0
0
aBv
(a v t) ??
(b)
0
aBv
2 ?
(c)
0
Bv
?
(d)
0
Bv
2 ?

Q 6.  A conducting square loop is placed in a magnetic field B with its plane perpendicular to the field.
Some how the sides of the loop start shrinking at a constant rate ?. The induced emf in the loop at
an instant when

its side is a, is
(a) 2a ?B  (b) a
2
?B  (c) 2a
2
?B  (d) a ?B
Q 7.  A conducting straight wire PQ of length l is fixed along a diameter of a non-conducting ring as
shown in, the figure. The ring is given a pure rolling motion on a horizontal surface such that its
centre of mass has a velocity v. There exists a uniform horizontal magnetic field B in horizontal
direction perpendicular to the plane of ring. The magnitude of induced emf in the wire PQ at the
position shown in the figure will be

(a) Bvl   (b) 2Bvl   (c) 3Bvl/2   (d) zero
Q 8.  A conducting rod of length L = 0.1 m is moving with a uniform speed v = 0.2 m/s on conducting
rails in a magnetic field B = 0.5 T as shown. On one side, the end of the rails is connected to a
capacitor of capacitance C = 20 ?F. Then the charges on the capacitor plates are

(a) q
A
= 0 = q
B
(b) q
A
= + 20 ?C and q
B
=-20 ?C
(c) q
A
= + 0.2 ?C and q
B
= -0.2 ?C  (d) q
A
=-0.2 ?C and q
B
= -0.2 ?C
Q 9.  A wire is bent in the form of a V shape and placed in a horizontal plane. There exists a uniform
magnetic field B perpendicular to the plane of the wire. A uniform conducting rod starts sliding
over the V shaped wire with a constant speed v as shown in the figure. If the wire has no
resistance, the current in rod will

(a) increase with time     (b) decrease with time
(c) remain constant     (d) always be zero
Q 10.  A square loop of side b is rotated in a constant magnetic field B at angular frequency ? as

shown
in the figure. What is the emf induced in it?

(a) b
2
B ? sin ?t (b) bB ?sin
2
?t (c) bB
2
? cos ?t (d) b
2
B ?
Q 11.  A uniform but time varying magnetic field exists in a cylindrical region as shown in the figure.
The direction of magnetic field is into the plane of the paper and its magnitude is decreasing at a
constant rate of 2 × 10
-3
T/s. A particle of charge 1 ?C

is moved slowly along a circle of radius 1 m
by an external force as shown in figure. The plane of the circle lies in the plane of the paper and it
is concentric with the

cylindrical region. The work done by the external force in moving this
charge along the circle will be

Page 4

Objective Questions
Single Correct Option
Q 1.  Two ends of an inductor of inductance L are connected to two parallel conducting wires. A rod of
length l and mass m is given velocity v
0
as shown. The whole system is placed in perpendicular
magnetic field B. Find the maximum current in the inductor, (neglect gravity and friction)

(a)
0
mv
L
(b)
0
m
v
L
(c)
2
0
mv
L
(d) None of these
Q 2.  A conducting rod is moving with a constant velocity v over the parallel conducting rails which are
connected at the ends through a resistor R and capacitor C as shown in the figure. Magnetic field
B is into the plane. Consider the following statements

(i) Current in loop AEFBA is anticlockwise (ii) Current in loop AEFBA is clockwise (iii) Current
through the capacitor is zero (iv) Energy stored in the capacitor is
2 2 2
1
CB L v
2

Which of the following options is correct?
(a) Statements (i) and (iii) are correct  (b) Statements (ii) and (iv) are correct
(c) Statements (i), (iii) and (iv) are correct  (d) None of these
Q 3.  A rod is rotating with a constant angular velocity ? about point O (its centre) in a magnetic field B
as shown. Which of the following figure correctly shows the distribution of charge inside the rod?

(a)    (b)    (c)    (d)
Q 4.  A straight conducting rod PQ is executing SHM in xy plane from x = - d to x = + d. Its mean
position is x = 0 and its length is along y-axis. There exists a uniform magnetic field B from x = -
d to x = 0 pointing inward normal to the paper and from x = 0 to = + d there exists another
uniform magnetic field of same magnitude B but pointing outward normal to the plane of the
paper. At the instant t = 0, the rod is at x ~ 0 and moving to the right. The induced emf ( ?)

across
the rod PQ vs time (t) graph will be

(a)      (b)
(c)      (d)
Q 5.  Two parallel long straight conductors lie on a smooth plane surface. Two other parallel conductors
rest on them at right angles so as to form a square of side a. A uniform magnetic field B exists at
right angles to the plane containing the conductors. Now conductors start moving outward with a
constant velocity v
0
at t = 0. Then induced current in the loop at any time t is ( ? is resistance per
unit length of the conductors)

(a)
0
0
aBv
(a v t) ??
(b)
0
aBv
2 ?
(c)
0
Bv
?
(d)
0
Bv
2 ?

Q 6.  A conducting square loop is placed in a magnetic field B with its plane perpendicular to the field.
Some how the sides of the loop start shrinking at a constant rate ?. The induced emf in the loop at
an instant when

its side is a, is
(a) 2a ?B  (b) a
2
?B  (c) 2a
2
?B  (d) a ?B
Q 7.  A conducting straight wire PQ of length l is fixed along a diameter of a non-conducting ring as
shown in, the figure. The ring is given a pure rolling motion on a horizontal surface such that its
centre of mass has a velocity v. There exists a uniform horizontal magnetic field B in horizontal
direction perpendicular to the plane of ring. The magnitude of induced emf in the wire PQ at the
position shown in the figure will be

(a) Bvl   (b) 2Bvl   (c) 3Bvl/2   (d) zero
Q 8.  A conducting rod of length L = 0.1 m is moving with a uniform speed v = 0.2 m/s on conducting
rails in a magnetic field B = 0.5 T as shown. On one side, the end of the rails is connected to a
capacitor of capacitance C = 20 ?F. Then the charges on the capacitor plates are

(a) q
A
= 0 = q
B
(b) q
A
= + 20 ?C and q
B
=-20 ?C
(c) q
A
= + 0.2 ?C and q
B
= -0.2 ?C  (d) q
A
=-0.2 ?C and q
B
= -0.2 ?C
Q 9.  A wire is bent in the form of a V shape and placed in a horizontal plane. There exists a uniform
magnetic field B perpendicular to the plane of the wire. A uniform conducting rod starts sliding
over the V shaped wire with a constant speed v as shown in the figure. If the wire has no
resistance, the current in rod will

(a) increase with time     (b) decrease with time
(c) remain constant     (d) always be zero
Q 10.  A square loop of side b is rotated in a constant magnetic field B at angular frequency ? as

shown
in the figure. What is the emf induced in it?

(a) b
2
B ? sin ?t (b) bB ?sin
2
?t (c) bB
2
? cos ?t (d) b
2
B ?
Q 11.  A uniform but time varying magnetic field exists in a cylindrical region as shown in the figure.
The direction of magnetic field is into the plane of the paper and its magnitude is decreasing at a
constant rate of 2 × 10
-3
T/s. A particle of charge 1 ?C

is moved slowly along a circle of radius 1 m
by an external force as shown in figure. The plane of the circle lies in the plane of the paper and it
is concentric with the

cylindrical region. The work done by the external force in moving this
charge along the circle will be

(a) zero  (b) 2 ? × 10
-9
J  (c) ? × 10
-9
J  (d) 4 ? × 10
-6
J
Q 12.  Switch S is closed at t = 0, in the circuit shown. The change in flux in the inductor (L = 500 mH)
from t = 0 to an instant when it reaches steady state is

(a) 2Wb   (b) 1.5 Wb   (c) 0 Wb  (d) None of the above
Q 13.  An L-R circuit is connected to a battery at time t = 0. The energy stored in the inductor reaches
half its maximum value at time
(a)
R2
ln
L 21
??
??
?
??
(b)
L 2 1
ln
R 2
??
?
??
??
(c)
L2
ln
R 21
??
??
?
??
(d)
R 2 1
ln
L 2
??
?
??
??

Q 14.  Electric charge q is distributed uniformly over a rod of length l. The rod is placed parallel to a long
wire carrying a current i. The separation between the rod and the wire is a. The force needed to
move the rod along its length with a uniform velocity v is
(a)
0
iqv
2a
?
?
(b)
0
iqv
4a
?
?
(c)
0
iqvl
2a
?
?
(d)
0
iqvl
4a
?
?

Q 15.  AB is an infinitely long wire placed in the plane of rectangular coil of dimensions as

shown in the
figure. Calculate the mutual inductance of wire AB and coil PQRS

(a)
0
b a
ln
2b
?
?
(b)
0
c b
ln
2a
?
?
(c)
0
2
abc
2 (b a)
?
??
(d) None of these
Q 16.  PQ is an infinite current carrying conductor. AB and CD are smooth conducting rods on which a
conductor EF moves with constant velocity v as shown. The force needed

to maintain constant
speed of EF is

(a)
2
0
Iv 1 (b)
ln
vR 2 (a)
?? ?
??
?
??
(b)
2
0
Iv v (a)
ln
R 2 (b)
?? ?
??
?
??
(c)
2
0
Iv v (b)
ln
R 2 (a)
?? ?
??
?
??
(d) None of these
Page 5

Objective Questions
Single Correct Option
Q 1.  Two ends of an inductor of inductance L are connected to two parallel conducting wires. A rod of
length l and mass m is given velocity v
0
as shown. The whole system is placed in perpendicular
magnetic field B. Find the maximum current in the inductor, (neglect gravity and friction)

(a)
0
mv
L
(b)
0
m
v
L
(c)
2
0
mv
L
(d) None of these
Q 2.  A conducting rod is moving with a constant velocity v over the parallel conducting rails which are
connected at the ends through a resistor R and capacitor C as shown in the figure. Magnetic field
B is into the plane. Consider the following statements

(i) Current in loop AEFBA is anticlockwise (ii) Current in loop AEFBA is clockwise (iii) Current
through the capacitor is zero (iv) Energy stored in the capacitor is
2 2 2
1
CB L v
2

Which of the following options is correct?
(a) Statements (i) and (iii) are correct  (b) Statements (ii) and (iv) are correct
(c) Statements (i), (iii) and (iv) are correct  (d) None of these
Q 3.  A rod is rotating with a constant angular velocity ? about point O (its centre) in a magnetic field B
as shown. Which of the following figure correctly shows the distribution of charge inside the rod?

(a)    (b)    (c)    (d)
Q 4.  A straight conducting rod PQ is executing SHM in xy plane from x = - d to x = + d. Its mean
position is x = 0 and its length is along y-axis. There exists a uniform magnetic field B from x = -
d to x = 0 pointing inward normal to the paper and from x = 0 to = + d there exists another
uniform magnetic field of same magnitude B but pointing outward normal to the plane of the
paper. At the instant t = 0, the rod is at x ~ 0 and moving to the right. The induced emf ( ?)

across
the rod PQ vs time (t) graph will be

(a)      (b)
(c)      (d)
Q 5.  Two parallel long straight conductors lie on a smooth plane surface. Two other parallel conductors
rest on them at right angles so as to form a square of side a. A uniform magnetic field B exists at
right angles to the plane containing the conductors. Now conductors start moving outward with a
constant velocity v
0
at t = 0. Then induced current in the loop at any time t is ( ? is resistance per
unit length of the conductors)

(a)
0
0
aBv
(a v t) ??
(b)
0
aBv
2 ?
(c)
0
Bv
?
(d)
0
Bv
2 ?

Q 6.  A conducting square loop is placed in a magnetic field B with its plane perpendicular to the field.
Some how the sides of the loop start shrinking at a constant rate ?. The induced emf in the loop at
an instant when

its side is a, is
(a) 2a ?B  (b) a
2
?B  (c) 2a
2
?B  (d) a ?B
Q 7.  A conducting straight wire PQ of length l is fixed along a diameter of a non-conducting ring as
shown in, the figure. The ring is given a pure rolling motion on a horizontal surface such that its
centre of mass has a velocity v. There exists a uniform horizontal magnetic field B in horizontal
direction perpendicular to the plane of ring. The magnitude of induced emf in the wire PQ at the
position shown in the figure will be

(a) Bvl   (b) 2Bvl   (c) 3Bvl/2   (d) zero
Q 8.  A conducting rod of length L = 0.1 m is moving with a uniform speed v = 0.2 m/s on conducting
rails in a magnetic field B = 0.5 T as shown. On one side, the end of the rails is connected to a
capacitor of capacitance C = 20 ?F. Then the charges on the capacitor plates are

(a) q
A
= 0 = q
B
(b) q
A
= + 20 ?C and q
B
=-20 ?C
(c) q
A
= + 0.2 ?C and q
B
= -0.2 ?C  (d) q
A
=-0.2 ?C and q
B
= -0.2 ?C
Q 9.  A wire is bent in the form of a V shape and placed in a horizontal plane. There exists a uniform
magnetic field B perpendicular to the plane of the wire. A uniform conducting rod starts sliding
over the V shaped wire with a constant speed v as shown in the figure. If the wire has no
resistance, the current in rod will

(a) increase with time     (b) decrease with time
(c) remain constant     (d) always be zero
Q 10.  A square loop of side b is rotated in a constant magnetic field B at angular frequency ? as

shown
in the figure. What is the emf induced in it?

(a) b
2
B ? sin ?t (b) bB ?sin
2
?t (c) bB
2
? cos ?t (d) b
2
B ?
Q 11.  A uniform but time varying magnetic field exists in a cylindrical region as shown in the figure.
The direction of magnetic field is into the plane of the paper and its magnitude is decreasing at a
constant rate of 2 × 10
-3
T/s. A particle of charge 1 ?C

is moved slowly along a circle of radius 1 m
by an external force as shown in figure. The plane of the circle lies in the plane of the paper and it
is concentric with the

cylindrical region. The work done by the external force in moving this
charge along the circle will be

(a) zero  (b) 2 ? × 10
-9
J  (c) ? × 10
-9
J  (d) 4 ? × 10
-6
J
Q 12.  Switch S is closed at t = 0, in the circuit shown. The change in flux in the inductor (L = 500 mH)
from t = 0 to an instant when it reaches steady state is

(a) 2Wb   (b) 1.5 Wb   (c) 0 Wb  (d) None of the above
Q 13.  An L-R circuit is connected to a battery at time t = 0. The energy stored in the inductor reaches
half its maximum value at time
(a)
R2
ln
L 21
??
??
?
??
(b)
L 2 1
ln
R 2
??
?
??
??
(c)
L2
ln
R 21
??
??
?
??
(d)
R 2 1
ln
L 2
??
?
??
??

Q 14.  Electric charge q is distributed uniformly over a rod of length l. The rod is placed parallel to a long
wire carrying a current i. The separation between the rod and the wire is a. The force needed to
move the rod along its length with a uniform velocity v is
(a)
0
iqv
2a
?
?
(b)
0
iqv
4a
?
?
(c)
0
iqvl
2a
?
?
(d)
0
iqvl
4a
?
?

Q 15.  AB is an infinitely long wire placed in the plane of rectangular coil of dimensions as

shown in the
figure. Calculate the mutual inductance of wire AB and coil PQRS

(a)
0
b a
ln
2b
?
?
(b)
0
c b
ln
2a
?
?
(c)
0
2
abc
2 (b a)
?
??
(d) None of these
Q 16.  PQ is an infinite current carrying conductor. AB and CD are smooth conducting rods on which a
conductor EF moves with constant velocity v as shown. The force needed

to maintain constant
speed of EF is

(a)
2
0
Iv 1 (b)
ln
vR 2 (a)
?? ?
??
?
??
(b)
2
0
Iv v (a)
ln
R 2 (b)
?? ?
??
?
??
(c)
2
0
Iv v (b)
ln
R 2 (a)
?? ?
??
?
??
(d) None of these
Q 17.  The figure shows a circular region of radius R occupied by a time varying magnetic field  B(t)
?
such that
dB
0
dt
? .

The magnitude of induced electric field at the point P at a distance r < R is

(a) decreasing with r     (b) increasing with r
(c) not varying with r     (d) varying as r
-2

Q 18.  Two circular loops P and Q are concentric and coplanar as shown in figure. The loop Q is smaller
than P. If the current I, flowing in loop P is decreasing with time, then the current I
2
in the loop Q

(a) flows in the same direction as that of P  (b) flows in the opposite direction as that of Q
(c) is zero      (d) None of these
Q 19.  In the circuit shown in figure the switch S is closed at t = 0. If V
L
is the voltage induced across the
inductor and i is the instantaneous current, the correct variation of V
L
versus i is given by

(a)  (b) (c) (d)
Q 20.  In the figure shown, a uniform magnetic field | B
?
| = 0.5T is perpendicular to the plane of circuit.
The sliding rod of length l = 0.25 m moves uniformly with constant speed v = 4ms
-1
. If the
resistance of the slides is 2 ?, then the current flowing through the sliding rod is

(a) 0.1 A   (b) 0.17 A   (c) 0.08 A   (d) 0.03 A
Q 21.  The figure shows a non-conducting ring of radius R carrying a charge q. In a circular region of
radius r, a uniform magnetic field B
?
perpendicular to the plane of

the ring varies at a constant rate
dB
dt
?? .

The torque acting on the ring is
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,

,

,

,

;