Electromagnetic Induction | Physics JEE Main questions with Solutions

Q 1 :

In a coil, the current changes from $- 2 A$ to $+ 2 A$ in 0.2 s and induces an emf 0.1 V. The self-inductance of the coil is: [2024]

4 mH
5 mH
2.5 mH
1 MH

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(2)

${(Emf)}_{induced} = - L \frac{d i}{d t}$

In magnitude form,

$| {Emf}_{ind} | = | (-) L \frac{d i}{d t} |$

$\Rightarrow 0.1 = \frac{(L) [+ 2 - (- 2)]}{0.2} \Rightarrow L = \frac{0.1 \times 0.2}{4} = 5 mH$

Q 2 :

The current in an inductor is given by $I = (3 t + 8)$ where $t$ is in second. The magnitude of induced emf produced in the inductor is 12 mV. The self-inductance of the inductor ________ mH. [2024]

(4) $| \in | = L \frac{d i}{d t}$

$i = | 3 t + 8 | \Rightarrow \frac{d i}{d t} = 3$

$ε = 12 mV$

$| ε | = L | \frac{d I}{d t} | \Rightarrow 12 = L \times 3$

$L = 4 mH$

Q 3 :

Two coils have mutual inductance 0.002H. The current changes in the first coil according to the relation $i = i_{0} \sin ω t$ , where $i_{0} = 5 A$ and $ω = 50 π$ rad/s. The maximum value of emf in the second coil is $\frac{π}{α}$ V. The value of $α$ is _____. [2024]

(2) $ϕ = M i = M i_{0} \sin ω t$

$EMF = - M \frac{d i}{d t} = - 0.002 (i_{0} ω \cos ω t)$

${EMF}_{\max} = i_{0} ω (0.002) = (5) (50 π) (0.002)$

${EMF}_{\max} = \frac{π}{2} V$

Q 4 :

Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is [2024]

$\frac{μ_{0} π b^{2}}{2 a}$
$\frac{μ_{0} π a^{2}}{2 b}$
$\frac{μ_{0}}{2 π} \cdot \frac{b^{2}}{a}$
$\frac{μ_{0}}{2 π} \cdot \frac{a^{2}}{b}$

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(2)

Magnetic flux through smaller loop, $ϕ = M i = B A$

$ϕ = (\frac{μ_{0} i}{2 b}) \cdot π a^{2} = M i$

$M = \frac{μ_{0} π a^{2}}{2 b}$

Q 5 :

A small square loop of wire of side L is placed inside a large square loop of wire of side $L (L = l^{2})$ . The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x} \times 10^{- 7}$ H, where $x =$ ____. [2024]

(128)

Flux linkage for inner loop.

$ϕ = B_{center} \cdot l^{2} = 4 \times \frac{μ_{0} i}{4 π \frac{L}{2}} (\sin 45 + \sin 45) l^{2}$

$ϕ = 2 \sqrt{2} \frac{μ_{0} i}{π L} l^{2}$

$M = \frac{ϕ}{i} = \frac{2 \sqrt{2} μ_{0} l^{2}}{π L} = 2 \sqrt{2} \frac{μ_{0}}{π}$

$= 2 \sqrt{2} \frac{4 π}{π} \times 10^{- 7} = \sqrt{128} \times 10^{- 7} H$

$\Rightarrow x = 128$

Q 6 :

Regarding self-inductance:

A. The self-inductance of the coil depends on its geometry.

B. Self-inductance does not depend on the permeability of the medium.

C. Self-induced e.m.f. opposes any change in the current in a circuit.

D. Self-inductance is electromagnetic analogue of mass in mechanics.

E. Work needs to be done against self-induced e.m.f. in establishing the current.

Choose the correct answer from the options given below: [2025]

A, B, C, D only
A, C, D, E only
A, B, C, E only
B, C, D, E only

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(2)

Self-inductance of coil

$L = \frac{μ_{0} μ_{r} N^{2}}{2 π R}$

Q 7 :

Consider $I_{1}$ and $I_{2}$ are the currents flowing simultaneously in two nearby coils 1 and 2, respectively. If $L_{1}$ = self-inductance of coil 1, $M_{12}$ = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be [2025]

$ε_{1} = - L_{1} \frac{d I_{1}}{d t} + M_{12} \frac{d I_{2}}{d t}$
$ε_{1} = - L_{1} \frac{d I_{1}}{d t} - M_{12} \frac{d I_{1}}{d t}$
$ε_{1} = - L_{1} \frac{d I_{1}}{d t} - M_{12} \frac{d I_{2}}{d t}$
$ε_{1} = - L_{1} \frac{d I_{2}}{d t} - M_{12} \frac{d I_{1}}{d t}$

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(3)

$ϕ_{1} = L_{1} I_{1} + M_{12} I_{2}$

$ε_{1} = - \frac{d ϕ_{1}}{d t} = - L_{1} \frac{d I_{1}}{d t} - M_{12} \frac{d I_{2}}{d t}$

Magnitude of induced emf due to self-inductance, $= \frac{L d I_{1}}{d t}$

Magnitude of induced emf due to mutual inductance, $= \frac{M d I_{2}}{d t}$

Q 8 :

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius $' R'$ is placed inside a large square loop of wire of side $L$ $(L > > R)$ . The loops are coplanar and their centres coincide. [2023]

$M = \frac{\sqrt{2} μ_{0} R^{2}}{L}$
$M = \frac{2 \sqrt{2} μ_{0} R}{L^{2}}$
$M = \frac{2 \sqrt{2} μ_{0} R^{2}}{L}$
$M = \frac{\sqrt{2} μ_{0} R}{L^{2}}$

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(3)

$ϕ = M i also ϕ = B A$

$ϕ = π R^{2} (4 \frac{μ_{0}}{4 π} \frac{i}{(L / 2)} \sqrt{2})$

$\Rightarrow M = \frac{2 \sqrt{2} μ_{0} R^{2}}{L}$

Q 9 :

A 12 V battery connected to a coil of resistance $6 Ω$ through a switch, drives a constant current in the circuit. The switch is opened in 1 ms. The emf induced across the coil is 20 V. The inductance of the coil is [2023]

5 mH
12 mH
8 mH
10 mH

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(4)

$Induced emf = - L \frac{d I}{d t}$

$\Rightarrow 20 = - L \frac{(0 - 2)}{10^{- 3}}$

$\Rightarrow L = 10 mH$

Q 10 :

Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively, are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _________ $\times 10^{- 8} H$ . (Take, $π^{2} = 10$ ) [2023]

(4)

$r_{1} = 1 cm, N_{1} = 10$

$r_{2} = 1000 cm, N_{2} = 200$

$ϕ_{1, 2} = M I_{2}$

$N_{2} {\vec{B}}_{2} \cdot N_{1} {\vec{A}}_{1} = M I_{2}$

$\Rightarrow N_{1} N_{2} \frac{μ_{0} I_{2}}{2 r_{2}} \cdot π r_{1}^{2} = M I_{2}$

$\Rightarrow M = \frac{10 \times 200 \times 4 π \times 10^{- 7} \times π \times {(0.01)}^{2}}{2 \times 10}$

$\Rightarrow M = 4 \times 10^{- 8}$

Q 11 :

Three identical coils $C_{1}$ , $C_{2}$ and $C_{3}$ are closely placed such that they share a common axis. $C_{2}$ is exactly midway. $C_{1}$ carries current $I$ in anti-clockwise direction while $C_{3}$ carries current $I$ in clockwise direction. An induced current flows through $C_{2}$ will be in clockwise direction when [2026]

$C_{1}$ moves towards $C_{2}$ and $C_{3}$ moves away from $C_{2}$
$C_{1}$ moves away from $C_{2}$ and $C_{3}$ moves towards $C_{2}$
$C_{1}$ and $C_{3}$ move with equal speeds towards $C_{2}$
$C_{1}$ and $C_{3}$ move with equal speeds away from $C_{2}$

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(1)

Magnetic field through the coil is

$\vec{B} = (B_{c_{2}} - B_{c_{1}}) \hat{i}$

$ϕ = (B_{c_{2}} - B_{c_{1}}) A$

$ε = \frac{- d ϕ}{d t}$

Find the direction according to Lenz's law.

If the coil moves away, then the magnetic field decreases and vice versa.

Correct Ans. (1)

Q 12 :

Match List – I with List – II

List I List II

A) AC generator I) Detects the presence of current in the circuit

B) Galvanometer II) Converts mechanical energy into electrical energy

C) Transformer III) Works on the principle of mutual induction in AC circuits

D) Zener Diode IV) Voltage regulator

Choose the correct answer from the options given below:

A – II, B – I, C – IV, D – III
A – II, B – I, C – III, D – IV
A – III, B – IV, C – II, D – I
A – III, B – I, C – II, D – IV

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(2)

Zener diode is used as voltage regulator.

Topic Question Set

Q 1 :

In a coil, the current changes from $- 2 A$ to $+ 2 A$ in 0.2 s and induces an emf 0.1 V. The self-inductance of the coil is: [2024]

Q 2 :

The current in an inductor is given by $I = (3 t + 8)$ where $t$ is in second. The magnitude of induced emf produced in the inductor is 12 mV. The self-inductance of the inductor ________ mH. [2024]

Q 3 :

Two coils have mutual inductance 0.002H. The current changes in the first coil according to the relation $i = i_{0} \sin ω t$ , where $i_{0} = 5 A$ and $ω = 50 π$ rad/s. The maximum value of emf in the second coil is $\frac{π}{α}$ V. The value of $α$ is _____. [2024]

Q 4 :

Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is [2024]

Q 5 :

A small square loop of wire of side L is placed inside a large square loop of wire of side $L (L = l^{2})$ . The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x} \times 10^{- 7}$ H, where $x =$ ____. [2024]

Q 7 :

Consider $I_{1}$ and $I_{2}$ are the currents flowing simultaneously in two nearby coils 1 and 2, respectively. If $L_{1}$ = self-inductance of coil 1, $M_{12}$ = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be [2025]

Q 8 :

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius $' R'$ is placed inside a large square loop of wire of side $L$ $(L > > R)$ . The loops are coplanar and their centres coincide. [2023]

Q 9 :

A 12 V battery connected to a coil of resistance $6 Ω$ through a switch, drives a constant current in the circuit. The switch is opened in 1 ms. The emf induced across the coil is 20 V. The inductance of the coil is [2023]

Q 10 :

Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively, are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _________ $\times 10^{- 8} H$ . (Take, $π^{2} = 10$ ) [2023]

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	List I		List II
A)	AC generator	I)	Detects the presence of current in the circuit
B)	Galvanometer	II)	Converts mechanical energy into electrical energy
C)	Transformer	III)	Works on the principle of mutual induction in AC circuits
D)	Zener Diode	IV)	Voltage regulator

Topic Question Set

Q 1 : In a coil, the current changes from -2A to +2A in 0.2 s and induces an emf 0.1 V. The self-inductance of the coil is: [2024]

Q 2 : The current in an inductor is given by I=(3t+8) where t is in second. The magnitude of induced emf produced in the inductor is 12 mV. The self-inductance of the inductor ________ mH. [2024]

Q 3 : Two coils have mutual inductance 0.002H. The current changes in the first coil according to the relation i=i0sinωt, where i0=5A and ω=50π rad/s. The maximum value of emf in the second coil is πα V. The value of α is _____. [2024]

Q 4 : Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is [2024]

Q 5 : A small square loop of wire of side L is placed inside a large square loop of wire of side L(L=l2). The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is x×10-7H, where x= ____. [2024]

Q 7 : Consider I1 and I2 are the currents flowing simultaneously in two nearby coils 1 and 2, respectively. If L1 = self-inductance of coil 1, M12 = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be [2025]

Q 8 : Find the mutual inductance in the arrangement, when a small circular loop of wire of radius 'R' is placed inside a large square loop of wire of side L (L>>R). The loops are coplanar and their centres coincide. [2023]

Q 9 : A 12 V battery connected to a coil of resistance 6 Ω through a switch, drives a constant current in the circuit. The switch is opened in 1 ms. The emf induced across the coil is 20 V. The inductance of the coil is [2023]

Q 10 : Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively, are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _________ ×10-8 H. (Take, π2=10) [2023]

Q 11 : Three identical coils C1, C2 and C3 are closely placed such that they share a common axis. C2 is exactly midway. C1 carries current I in anti-clockwise direction while C3 carries current I in clockwise direction. An induced current flows through C2 will be in clockwise direction when [2026]

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Q 1 :

In a coil, the current changes from $- 2 A$ to $+ 2 A$ in 0.2 s and induces an emf 0.1 V. The self-inductance of the coil is: [2024]

Q 2 :

The current in an inductor is given by $I = (3 t + 8)$ where $t$ is in second. The magnitude of induced emf produced in the inductor is 12 mV. The self-inductance of the inductor ________ mH. [2024]

Q 3 :

Two coils have mutual inductance 0.002H. The current changes in the first coil according to the relation $i = i_{0} \sin ω t$ , where $i_{0} = 5 A$ and $ω = 50 π$ rad/s. The maximum value of emf in the second coil is $\frac{π}{α}$ V. The value of $α$ is _____. [2024]

Q 4 :

Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is [2024]

Q 5 :

A small square loop of wire of side L is placed inside a large square loop of wire of side $L (L = l^{2})$ . The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x} \times 10^{- 7}$ H, where $x =$ ____. [2024]

Q 7 :

Consider $I_{1}$ and $I_{2}$ are the currents flowing simultaneously in two nearby coils 1 and 2, respectively. If $L_{1}$ = self-inductance of coil 1, $M_{12}$ = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be [2025]

Q 8 :

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius $' R'$ is placed inside a large square loop of wire of side $L$ $(L > > R)$ . The loops are coplanar and their centres coincide. [2023]

Q 9 :

A 12 V battery connected to a coil of resistance $6 Ω$ through a switch, drives a constant current in the circuit. The switch is opened in 1 ms. The emf induced across the coil is 20 V. The inductance of the coil is [2023]

Q 10 :

Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively, are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _________ $\times 10^{- 8} H$ . (Take, $π^{2} = 10$ ) [2023]