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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4

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

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]

0%

(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]

0%

(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]

0%

(128)

Flux linkage for inner loop.

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

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

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

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

$\Rightarrow x = 128$

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]

0%

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]

0%

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]

0%

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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]

0%

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]

0%

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]

0%

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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]