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]

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(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]

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(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]

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(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]

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(4)

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

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

$ϕ_{1, 2} = M I_{2}$

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

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

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

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

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]

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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]

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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]

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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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