DC Pandey Solutions (JEE Main): Electromagnetic Induction | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


 
Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Faraday ’s Law and Motional Emf 
Q 1.  A wire in the form of a circular loop of radius 10 cm lies in a plane normal to a magnetic field of 
100 T. If this wire is pulled to take a square shape in the same plane in 0.1 s, find the average 
induced emf in the loop. 
Q 2.  A closed coil consists of 500 turns has area 4 cm
2
 and a resistance of 50 ?.
 
The coil is kept with its 
plane perpendicular to a uniform magnetic field of 0.2 Wb/m
2
. Calculate the amount of charge 
flowing through the coil if it is rotated through 180°. 
Q 3.  A small coil is introduced between the poles of an electromagnet so that its axis coincides with the 
magnetic field direction. The cross-sectional area of the coil is equal to S = 3.0 mm
2
, the number 
of turns is N = 60. When the coil turns through 180° about its diameter, a galvanometer connected 
to the coil indicates a charge q = 4.5 ?C
 
flowing through it. Find the magnetic induction 
magnitude between the poles, provided the total resistance of the electric circuit equals R = 40 ?. 
Q 4.  The magnetic field in a certain region is given by 
3
ˆˆ
B (4.0i 1.8k) 10 T
?
? ? ?
?
.
 
How much flux passes 
through a 5.0 cm
2
 area loop in this region if the loop lies flat on the x-y plane? 
Q 5.  A horizontal wire 0.8 m long is falling at a speed of 5 m/s perpendicular to a uniform magnetic 
field of 1.1 T, which is directed from east to west. Calculate the magnitude of the induced emf. Is 
the north or south end of the wire positive? 
Q 6.  The magnetic field through a single loop of wire, 12 cm in radius and of 8.5 ? resistance, changes 
with time as shown in figure. Calculate the emf in the loop as a function of time. Consider the time 
intervals 
 
  (a) t = 0 to t = 2.0s,  (b) t = 2.0s to t = 4.0s,  (c) t = 4.0s to t = 6.0s.  
  The magnetic field is perpendicular to the plane of the loop. 
Q 7.  A square loop of wire with resistance R is moved at constant speed v across a uniform magnetic 
field confined to a square region whose sides are twice the lengths of those of the square loop. 
 
Page 2


 
Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Faraday ’s Law and Motional Emf 
Q 1.  A wire in the form of a circular loop of radius 10 cm lies in a plane normal to a magnetic field of 
100 T. If this wire is pulled to take a square shape in the same plane in 0.1 s, find the average 
induced emf in the loop. 
Q 2.  A closed coil consists of 500 turns has area 4 cm
2
 and a resistance of 50 ?.
 
The coil is kept with its 
plane perpendicular to a uniform magnetic field of 0.2 Wb/m
2
. Calculate the amount of charge 
flowing through the coil if it is rotated through 180°. 
Q 3.  A small coil is introduced between the poles of an electromagnet so that its axis coincides with the 
magnetic field direction. The cross-sectional area of the coil is equal to S = 3.0 mm
2
, the number 
of turns is N = 60. When the coil turns through 180° about its diameter, a galvanometer connected 
to the coil indicates a charge q = 4.5 ?C
 
flowing through it. Find the magnetic induction 
magnitude between the poles, provided the total resistance of the electric circuit equals R = 40 ?. 
Q 4.  The magnetic field in a certain region is given by 
3
ˆˆ
B (4.0i 1.8k) 10 T
?
? ? ?
?
.
 
How much flux passes 
through a 5.0 cm
2
 area loop in this region if the loop lies flat on the x-y plane? 
Q 5.  A horizontal wire 0.8 m long is falling at a speed of 5 m/s perpendicular to a uniform magnetic 
field of 1.1 T, which is directed from east to west. Calculate the magnitude of the induced emf. Is 
the north or south end of the wire positive? 
Q 6.  The magnetic field through a single loop of wire, 12 cm in radius and of 8.5 ? resistance, changes 
with time as shown in figure. Calculate the emf in the loop as a function of time. Consider the time 
intervals 
 
  (a) t = 0 to t = 2.0s,  (b) t = 2.0s to t = 4.0s,  (c) t = 4.0s to t = 6.0s.  
  The magnetic field is perpendicular to the plane of the loop. 
Q 7.  A square loop of wire with resistance R is moved at constant speed v across a uniform magnetic 
field confined to a square region whose sides are twice the lengths of those of the square loop. 
 
(a) Sketch a graph of the external force F needed to move the loop at constant speed, as a function 
of the co-ordinate x, from x = - 2L to x = + 2L. (The co-ordinate x is measured from the centre of 
the magnetic field region to the centre of the loop. It is negative when the centre of the loop is to 
the left of the centre of the magnetic field region. Take positive force to be to the right). 
(b) Sketch a graph of the induced current in the loop as a function of x. Take counterclockwise 
currents to be positive. 
Q 8.  A square frame with side a and a long straight wire carrying a current i are located in the same 
plane as shown in figure. The frame translates to the right with a constant velocity v. Find the emf 
induced in the frame as a function of distance x. 
 
Q 9.  In figure a wire perpendicular to a long straight wire is moving parallel to the later with a speed v 
= 10 m/s in the direction of the current flowing in the later. The current is 10 A. What is the 
magnitude of the potential difference between the ends of the moving wire? 
 
Q 10.  As shown in figure, a metal rod completes the circuit. The circuit area is perpendicular to a 
magnetic field with B = 0.15 T. If the resistance of the total circuit is 3 ?, how large a force is 
needed to move the rod as indicated with a constant speed of 2 m/s ? 
 
Q 11.  Two parallel rails with negligible resistance are 10.0 cm apart and are connected by a 5.00 ? 
resistor. The circuit also contains two metal rods having resistance of 10.0 ? and 15.0 ? sliding 
along the rails. The rods are pulled away from the resistor at constant speeds 8.00 m/s and 4.00 
m/s respectively. A uniform magnetic field of magnitude 0.010T is applied perpendicular to the 
plane of the rails. Determine the current in the 5.00 ? resistor. 
Page 3


 
Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Faraday ’s Law and Motional Emf 
Q 1.  A wire in the form of a circular loop of radius 10 cm lies in a plane normal to a magnetic field of 
100 T. If this wire is pulled to take a square shape in the same plane in 0.1 s, find the average 
induced emf in the loop. 
Q 2.  A closed coil consists of 500 turns has area 4 cm
2
 and a resistance of 50 ?.
 
The coil is kept with its 
plane perpendicular to a uniform magnetic field of 0.2 Wb/m
2
. Calculate the amount of charge 
flowing through the coil if it is rotated through 180°. 
Q 3.  A small coil is introduced between the poles of an electromagnet so that its axis coincides with the 
magnetic field direction. The cross-sectional area of the coil is equal to S = 3.0 mm
2
, the number 
of turns is N = 60. When the coil turns through 180° about its diameter, a galvanometer connected 
to the coil indicates a charge q = 4.5 ?C
 
flowing through it. Find the magnetic induction 
magnitude between the poles, provided the total resistance of the electric circuit equals R = 40 ?. 
Q 4.  The magnetic field in a certain region is given by 
3
ˆˆ
B (4.0i 1.8k) 10 T
?
? ? ?
?
.
 
How much flux passes 
through a 5.0 cm
2
 area loop in this region if the loop lies flat on the x-y plane? 
Q 5.  A horizontal wire 0.8 m long is falling at a speed of 5 m/s perpendicular to a uniform magnetic 
field of 1.1 T, which is directed from east to west. Calculate the magnitude of the induced emf. Is 
the north or south end of the wire positive? 
Q 6.  The magnetic field through a single loop of wire, 12 cm in radius and of 8.5 ? resistance, changes 
with time as shown in figure. Calculate the emf in the loop as a function of time. Consider the time 
intervals 
 
  (a) t = 0 to t = 2.0s,  (b) t = 2.0s to t = 4.0s,  (c) t = 4.0s to t = 6.0s.  
  The magnetic field is perpendicular to the plane of the loop. 
Q 7.  A square loop of wire with resistance R is moved at constant speed v across a uniform magnetic 
field confined to a square region whose sides are twice the lengths of those of the square loop. 
 
(a) Sketch a graph of the external force F needed to move the loop at constant speed, as a function 
of the co-ordinate x, from x = - 2L to x = + 2L. (The co-ordinate x is measured from the centre of 
the magnetic field region to the centre of the loop. It is negative when the centre of the loop is to 
the left of the centre of the magnetic field region. Take positive force to be to the right). 
(b) Sketch a graph of the induced current in the loop as a function of x. Take counterclockwise 
currents to be positive. 
Q 8.  A square frame with side a and a long straight wire carrying a current i are located in the same 
plane as shown in figure. The frame translates to the right with a constant velocity v. Find the emf 
induced in the frame as a function of distance x. 
 
Q 9.  In figure a wire perpendicular to a long straight wire is moving parallel to the later with a speed v 
= 10 m/s in the direction of the current flowing in the later. The current is 10 A. What is the 
magnitude of the potential difference between the ends of the moving wire? 
 
Q 10.  As shown in figure, a metal rod completes the circuit. The circuit area is perpendicular to a 
magnetic field with B = 0.15 T. If the resistance of the total circuit is 3 ?, how large a force is 
needed to move the rod as indicated with a constant speed of 2 m/s ? 
 
Q 11.  Two parallel rails with negligible resistance are 10.0 cm apart and are connected by a 5.00 ? 
resistor. The circuit also contains two metal rods having resistance of 10.0 ? and 15.0 ? sliding 
along the rails. The rods are pulled away from the resistor at constant speeds 8.00 m/s and 4.00 
m/s respectively. A uniform magnetic field of magnitude 0.010T is applied perpendicular to the 
plane of the rails. Determine the current in the 5.00 ? resistor. 
 
  Self Inductance 
Q 12.  The inductor shown in figure has inductance 0.54 H and carries a current in the direction shown 
that is decreasing at a uniform rate, di/dt = - 0.030 A/s: 
 
(a) Find the self-induced emf. 
  (b) Which end of the inductor, a or b, is at a higher potential? 
Q 13.  The current (in Ampere) in an inductor is given by I = 5 + 16t, where t is in seconds. The self-
induced emf in it is 10 mV. Find : 
(a) the self-inductance, and 
(b) the energy stored in the inductor and the power supplied to it at t = 1 s 
Q 14.  The potential difference across a 150 mH inductor as a function of time is shown in figure. 
Assume that the initial value of the current in the inductor is zero. What is the current when t = 2.0 
ms? and t = 4.0ms? 
 
Q 15.  At the instant when the current in an inductor is increasing at a rate of 0.0640 A/s, the magnitude 
of the self-induced emf is 0.0160 V. 
  (a) What is the inductance of the inductor? 
(b) If the inductor is a solenoid with 400 turns, what is the average magnetic flux through each 
turn when the current is 0.720 A? 
  Mutual inductance 
Q 16.  Calculate the mutual inductance between two coils when a current of 4 A changes to 12 A in 0.5 s 
in primary and induces an emf of 50 mV in the secondary. Also calculate the induced emf in the 
secondary if current in the primary changes from 3 A to 9 A is 0.02 s. 
Q 17.  A coil has 600 turns which produces 5 × 10
-3
 Wb/turn of flux when 3 A current flows in the wire. 
This produced 6 × 10
-3
 Wb/turn in 1000 turns secondary coil. When the switch is opened the 
current drops to zero in 0.2 s in primary. Find : 
  (a) mutual inductance,    (b) the induced emf in the secondary,  
  (c) the self inductance of the primary coil.  
Page 4


 
Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Faraday ’s Law and Motional Emf 
Q 1.  A wire in the form of a circular loop of radius 10 cm lies in a plane normal to a magnetic field of 
100 T. If this wire is pulled to take a square shape in the same plane in 0.1 s, find the average 
induced emf in the loop. 
Q 2.  A closed coil consists of 500 turns has area 4 cm
2
 and a resistance of 50 ?.
 
The coil is kept with its 
plane perpendicular to a uniform magnetic field of 0.2 Wb/m
2
. Calculate the amount of charge 
flowing through the coil if it is rotated through 180°. 
Q 3.  A small coil is introduced between the poles of an electromagnet so that its axis coincides with the 
magnetic field direction. The cross-sectional area of the coil is equal to S = 3.0 mm
2
, the number 
of turns is N = 60. When the coil turns through 180° about its diameter, a galvanometer connected 
to the coil indicates a charge q = 4.5 ?C
 
flowing through it. Find the magnetic induction 
magnitude between the poles, provided the total resistance of the electric circuit equals R = 40 ?. 
Q 4.  The magnetic field in a certain region is given by 
3
ˆˆ
B (4.0i 1.8k) 10 T
?
? ? ?
?
.
 
How much flux passes 
through a 5.0 cm
2
 area loop in this region if the loop lies flat on the x-y plane? 
Q 5.  A horizontal wire 0.8 m long is falling at a speed of 5 m/s perpendicular to a uniform magnetic 
field of 1.1 T, which is directed from east to west. Calculate the magnitude of the induced emf. Is 
the north or south end of the wire positive? 
Q 6.  The magnetic field through a single loop of wire, 12 cm in radius and of 8.5 ? resistance, changes 
with time as shown in figure. Calculate the emf in the loop as a function of time. Consider the time 
intervals 
 
  (a) t = 0 to t = 2.0s,  (b) t = 2.0s to t = 4.0s,  (c) t = 4.0s to t = 6.0s.  
  The magnetic field is perpendicular to the plane of the loop. 
Q 7.  A square loop of wire with resistance R is moved at constant speed v across a uniform magnetic 
field confined to a square region whose sides are twice the lengths of those of the square loop. 
 
(a) Sketch a graph of the external force F needed to move the loop at constant speed, as a function 
of the co-ordinate x, from x = - 2L to x = + 2L. (The co-ordinate x is measured from the centre of 
the magnetic field region to the centre of the loop. It is negative when the centre of the loop is to 
the left of the centre of the magnetic field region. Take positive force to be to the right). 
(b) Sketch a graph of the induced current in the loop as a function of x. Take counterclockwise 
currents to be positive. 
Q 8.  A square frame with side a and a long straight wire carrying a current i are located in the same 
plane as shown in figure. The frame translates to the right with a constant velocity v. Find the emf 
induced in the frame as a function of distance x. 
 
Q 9.  In figure a wire perpendicular to a long straight wire is moving parallel to the later with a speed v 
= 10 m/s in the direction of the current flowing in the later. The current is 10 A. What is the 
magnitude of the potential difference between the ends of the moving wire? 
 
Q 10.  As shown in figure, a metal rod completes the circuit. The circuit area is perpendicular to a 
magnetic field with B = 0.15 T. If the resistance of the total circuit is 3 ?, how large a force is 
needed to move the rod as indicated with a constant speed of 2 m/s ? 
 
Q 11.  Two parallel rails with negligible resistance are 10.0 cm apart and are connected by a 5.00 ? 
resistor. The circuit also contains two metal rods having resistance of 10.0 ? and 15.0 ? sliding 
along the rails. The rods are pulled away from the resistor at constant speeds 8.00 m/s and 4.00 
m/s respectively. A uniform magnetic field of magnitude 0.010T is applied perpendicular to the 
plane of the rails. Determine the current in the 5.00 ? resistor. 
 
  Self Inductance 
Q 12.  The inductor shown in figure has inductance 0.54 H and carries a current in the direction shown 
that is decreasing at a uniform rate, di/dt = - 0.030 A/s: 
 
(a) Find the self-induced emf. 
  (b) Which end of the inductor, a or b, is at a higher potential? 
Q 13.  The current (in Ampere) in an inductor is given by I = 5 + 16t, where t is in seconds. The self-
induced emf in it is 10 mV. Find : 
(a) the self-inductance, and 
(b) the energy stored in the inductor and the power supplied to it at t = 1 s 
Q 14.  The potential difference across a 150 mH inductor as a function of time is shown in figure. 
Assume that the initial value of the current in the inductor is zero. What is the current when t = 2.0 
ms? and t = 4.0ms? 
 
Q 15.  At the instant when the current in an inductor is increasing at a rate of 0.0640 A/s, the magnitude 
of the self-induced emf is 0.0160 V. 
  (a) What is the inductance of the inductor? 
(b) If the inductor is a solenoid with 400 turns, what is the average magnetic flux through each 
turn when the current is 0.720 A? 
  Mutual inductance 
Q 16.  Calculate the mutual inductance between two coils when a current of 4 A changes to 12 A in 0.5 s 
in primary and induces an emf of 50 mV in the secondary. Also calculate the induced emf in the 
secondary if current in the primary changes from 3 A to 9 A is 0.02 s. 
Q 17.  A coil has 600 turns which produces 5 × 10
-3
 Wb/turn of flux when 3 A current flows in the wire. 
This produced 6 × 10
-3
 Wb/turn in 1000 turns secondary coil. When the switch is opened the 
current drops to zero in 0.2 s in primary. Find : 
  (a) mutual inductance,    (b) the induced emf in the secondary,  
  (c) the self inductance of the primary coil.  
Q 18.  Two coils have mutual inductance M = 3.25 × 10
-4
 H The current i
1
 in the first coil increases at a 
uniform rate of 830 A/s. 
  (a) What is the magnitude of the induced emf in the second coil? Is it constant? 
(b) Suppose that the current described is in the second coil rather than the first. What is the 
induced emf in the first coil? 
Q 19.  Two toroidal solenoids are wound around the same pipe so that the magnetic field of one passes 
through the turns of the other. Solenoid 1 has 700 turns and solenoid 2 has 400 turns. When the 
current in solenoid 1 is 6.52 A, the average flux through each turn of solenoid 2 is 0.0320 Wb. 
  (a) What is the mutual inductance of the pair of solenoids? 
(b) When the current in solenoid 2 is 2.54 A, what is the average flux through each turn of 
solenoid 1 ? 
  L-R Circuits 
Q 20.  Show that L/R has units of time.  
Q 21.  A coil of inductance 1 H and resistance 10? is connected to a resistanceless battery of emf 50 V at 
time t = 0. Calculate the ratio of the rate at which magnetic energy is stored in the coil to the rate 
at which energy is supplied by the battery at t = 0.1 s. 
Q 22.  A coil of inductance 2 H and resistance 10 ? are in a series circuit with an open key and a cell of 
constant 100 V with negligible resistance. At time t = 0, the key is closed. Find : 
  (a) the time constant of the circuit. 
  (b) the maximum steady current in the circuit. 
  (c) the current in the circuit at t = 1 s. 
Q 23.  A 3.56 H inductor is placed in series with a 12.8 ?
 
resistor. An emf of 3.24 Vis then suddenly 
applied across the RL combination. 
(a) At 0.278 s after the emf is applied what is the rate at which energy is being delivered by the 
battery? 
  (b) At 0.278 s, at what rate is energy appearing as thermal energy in the resistor? 
  (c) At 0.278 s, at what rate is energy being stored in the magnetic field? 
Q 24.  An inductor with an inductance of 2.50 H and a resistance of 8.00 ? is connected to the terminals 
of a battery with an emf of 6.00 V and negligible internal resistance. Find 
  (a) the initial rate of increase of current in the circuit, 
  (b) the rate of increase of current at the instant when the current is 0.500 A, 
  (c) the current 0.250 s after the circuit is closed, 
  (d) the final steady state current. 
Q 25.  A 35.0 V battery with negligible internal resistance, a 50.0 ? resistor, and a 1.25 mH inductor 
with negligible resistance are all connected in series with an open switch. The switch is suddenly 
closed 
(a) How long after closing the switch will the current through the inductor reach one-half of its 
maximum value? 
(b) How long after closing the switch will the energy stored in the inductor reach one-half of its 
maximum value? 
Page 5


 
Exercises 
For JEE Main 
  Subjective Questions 
  Note You can take approximations in the answers. 
  Faraday ’s Law and Motional Emf 
Q 1.  A wire in the form of a circular loop of radius 10 cm lies in a plane normal to a magnetic field of 
100 T. If this wire is pulled to take a square shape in the same plane in 0.1 s, find the average 
induced emf in the loop. 
Q 2.  A closed coil consists of 500 turns has area 4 cm
2
 and a resistance of 50 ?.
 
The coil is kept with its 
plane perpendicular to a uniform magnetic field of 0.2 Wb/m
2
. Calculate the amount of charge 
flowing through the coil if it is rotated through 180°. 
Q 3.  A small coil is introduced between the poles of an electromagnet so that its axis coincides with the 
magnetic field direction. The cross-sectional area of the coil is equal to S = 3.0 mm
2
, the number 
of turns is N = 60. When the coil turns through 180° about its diameter, a galvanometer connected 
to the coil indicates a charge q = 4.5 ?C
 
flowing through it. Find the magnetic induction 
magnitude between the poles, provided the total resistance of the electric circuit equals R = 40 ?. 
Q 4.  The magnetic field in a certain region is given by 
3
ˆˆ
B (4.0i 1.8k) 10 T
?
? ? ?
?
.
 
How much flux passes 
through a 5.0 cm
2
 area loop in this region if the loop lies flat on the x-y plane? 
Q 5.  A horizontal wire 0.8 m long is falling at a speed of 5 m/s perpendicular to a uniform magnetic 
field of 1.1 T, which is directed from east to west. Calculate the magnitude of the induced emf. Is 
the north or south end of the wire positive? 
Q 6.  The magnetic field through a single loop of wire, 12 cm in radius and of 8.5 ? resistance, changes 
with time as shown in figure. Calculate the emf in the loop as a function of time. Consider the time 
intervals 
 
  (a) t = 0 to t = 2.0s,  (b) t = 2.0s to t = 4.0s,  (c) t = 4.0s to t = 6.0s.  
  The magnetic field is perpendicular to the plane of the loop. 
Q 7.  A square loop of wire with resistance R is moved at constant speed v across a uniform magnetic 
field confined to a square region whose sides are twice the lengths of those of the square loop. 
 
(a) Sketch a graph of the external force F needed to move the loop at constant speed, as a function 
of the co-ordinate x, from x = - 2L to x = + 2L. (The co-ordinate x is measured from the centre of 
the magnetic field region to the centre of the loop. It is negative when the centre of the loop is to 
the left of the centre of the magnetic field region. Take positive force to be to the right). 
(b) Sketch a graph of the induced current in the loop as a function of x. Take counterclockwise 
currents to be positive. 
Q 8.  A square frame with side a and a long straight wire carrying a current i are located in the same 
plane as shown in figure. The frame translates to the right with a constant velocity v. Find the emf 
induced in the frame as a function of distance x. 
 
Q 9.  In figure a wire perpendicular to a long straight wire is moving parallel to the later with a speed v 
= 10 m/s in the direction of the current flowing in the later. The current is 10 A. What is the 
magnitude of the potential difference between the ends of the moving wire? 
 
Q 10.  As shown in figure, a metal rod completes the circuit. The circuit area is perpendicular to a 
magnetic field with B = 0.15 T. If the resistance of the total circuit is 3 ?, how large a force is 
needed to move the rod as indicated with a constant speed of 2 m/s ? 
 
Q 11.  Two parallel rails with negligible resistance are 10.0 cm apart and are connected by a 5.00 ? 
resistor. The circuit also contains two metal rods having resistance of 10.0 ? and 15.0 ? sliding 
along the rails. The rods are pulled away from the resistor at constant speeds 8.00 m/s and 4.00 
m/s respectively. A uniform magnetic field of magnitude 0.010T is applied perpendicular to the 
plane of the rails. Determine the current in the 5.00 ? resistor. 
 
  Self Inductance 
Q 12.  The inductor shown in figure has inductance 0.54 H and carries a current in the direction shown 
that is decreasing at a uniform rate, di/dt = - 0.030 A/s: 
 
(a) Find the self-induced emf. 
  (b) Which end of the inductor, a or b, is at a higher potential? 
Q 13.  The current (in Ampere) in an inductor is given by I = 5 + 16t, where t is in seconds. The self-
induced emf in it is 10 mV. Find : 
(a) the self-inductance, and 
(b) the energy stored in the inductor and the power supplied to it at t = 1 s 
Q 14.  The potential difference across a 150 mH inductor as a function of time is shown in figure. 
Assume that the initial value of the current in the inductor is zero. What is the current when t = 2.0 
ms? and t = 4.0ms? 
 
Q 15.  At the instant when the current in an inductor is increasing at a rate of 0.0640 A/s, the magnitude 
of the self-induced emf is 0.0160 V. 
  (a) What is the inductance of the inductor? 
(b) If the inductor is a solenoid with 400 turns, what is the average magnetic flux through each 
turn when the current is 0.720 A? 
  Mutual inductance 
Q 16.  Calculate the mutual inductance between two coils when a current of 4 A changes to 12 A in 0.5 s 
in primary and induces an emf of 50 mV in the secondary. Also calculate the induced emf in the 
secondary if current in the primary changes from 3 A to 9 A is 0.02 s. 
Q 17.  A coil has 600 turns which produces 5 × 10
-3
 Wb/turn of flux when 3 A current flows in the wire. 
This produced 6 × 10
-3
 Wb/turn in 1000 turns secondary coil. When the switch is opened the 
current drops to zero in 0.2 s in primary. Find : 
  (a) mutual inductance,    (b) the induced emf in the secondary,  
  (c) the self inductance of the primary coil.  
Q 18.  Two coils have mutual inductance M = 3.25 × 10
-4
 H The current i
1
 in the first coil increases at a 
uniform rate of 830 A/s. 
  (a) What is the magnitude of the induced emf in the second coil? Is it constant? 
(b) Suppose that the current described is in the second coil rather than the first. What is the 
induced emf in the first coil? 
Q 19.  Two toroidal solenoids are wound around the same pipe so that the magnetic field of one passes 
through the turns of the other. Solenoid 1 has 700 turns and solenoid 2 has 400 turns. When the 
current in solenoid 1 is 6.52 A, the average flux through each turn of solenoid 2 is 0.0320 Wb. 
  (a) What is the mutual inductance of the pair of solenoids? 
(b) When the current in solenoid 2 is 2.54 A, what is the average flux through each turn of 
solenoid 1 ? 
  L-R Circuits 
Q 20.  Show that L/R has units of time.  
Q 21.  A coil of inductance 1 H and resistance 10? is connected to a resistanceless battery of emf 50 V at 
time t = 0. Calculate the ratio of the rate at which magnetic energy is stored in the coil to the rate 
at which energy is supplied by the battery at t = 0.1 s. 
Q 22.  A coil of inductance 2 H and resistance 10 ? are in a series circuit with an open key and a cell of 
constant 100 V with negligible resistance. At time t = 0, the key is closed. Find : 
  (a) the time constant of the circuit. 
  (b) the maximum steady current in the circuit. 
  (c) the current in the circuit at t = 1 s. 
Q 23.  A 3.56 H inductor is placed in series with a 12.8 ?
 
resistor. An emf of 3.24 Vis then suddenly 
applied across the RL combination. 
(a) At 0.278 s after the emf is applied what is the rate at which energy is being delivered by the 
battery? 
  (b) At 0.278 s, at what rate is energy appearing as thermal energy in the resistor? 
  (c) At 0.278 s, at what rate is energy being stored in the magnetic field? 
Q 24.  An inductor with an inductance of 2.50 H and a resistance of 8.00 ? is connected to the terminals 
of a battery with an emf of 6.00 V and negligible internal resistance. Find 
  (a) the initial rate of increase of current in the circuit, 
  (b) the rate of increase of current at the instant when the current is 0.500 A, 
  (c) the current 0.250 s after the circuit is closed, 
  (d) the final steady state current. 
Q 25.  A 35.0 V battery with negligible internal resistance, a 50.0 ? resistor, and a 1.25 mH inductor 
with negligible resistance are all connected in series with an open switch. The switch is suddenly 
closed 
(a) How long after closing the switch will the current through the inductor reach one-half of its 
maximum value? 
(b) How long after closing the switch will the energy stored in the inductor reach one-half of its 
maximum value? 
Q 26.  A solenoid of inductance L with resistance r is connected in parallel to a resistance R. A battery of 
emf E and of negligible internal resistance is connected across the parallel combination as shown 
in the figure. At time t = 0, switch S is opened, calculate 
 
  (a) current through the solenoid after the switch is opened. 
  (b) amount of heat generated in the solenoid.   
Q 27.  In the given circuit, find the current through the 5 mH inductor in steady state. 
 
Q 28.  An inductor of inductance L = 400 mH and resistors R
1
 = 2 ? and R
2
 = 2 ?
 
are connected to a 
battery of emf E = 12 Vas shown in the figure. The internal resistance of the battery is negligible. 
The switch 5 is closed at time t = 0. 
 
What is the potential drop across L as a function of time? After the steady state is reached, the 
switch is opened. What is the direction and the magnitude of current through R
1
 as a function of 
time? 
   L-C Oscillations  
Q 29.  In an oscillating L-C circuit in which C = 4.00 ?F, the maximum potential difference across the 
capacitor during the oscillations is 1.50 V and the maximum current through the inductor is 50.0 
mA. 
  (a) What is the inductance L ? 
  (b) What is the frequency of the oscillations? 
  (c) How much time does the charge on the capacitor take to rise from zero to its maximum value? 
Q 30.  In the L-C circuit shown, C = 1 ?F. With capacitor charged to 100 V, switch S is suddenly closed 
at time t = 0. The circuit then oscillates at 10
3 
Hz.