(C) According to Faraday's law of electromagnetic induction,the induced $emf$ $(E)$ is given by the negative rate of change of magnetic flux: $E = -\f

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(C) According to Faraday's law of electromagnetic induction,the induced $emf$ $(E)$ is given by the negative rate of change of magnetic flux: $E = -\frac{d\phi}{dt}$.Given $\phi = (3t^2 + 2t + 3) \times 10^{-3} \ Wb$ (since $\phi$ is in $mWb$).Taking the derivative with respect to time $t$:$\frac{d\phi}{dt} = \frac{d}{dt}(3t^2 + 2t + 3) \times 10^{-3} = (6t + 2) \times 10^{-3} \ Wb/s$.Thus,the induced $emf$ is $E = -(6t + 2) \times 10^{-3} \ V = -(6t + 2) \ mV$.The magnitude of the induced $emf$ at $t = 2 \ s$ is:$|E| = |-(6(2) + 2)| = |-(12 + 2)| = |-14| = 14 \ mV$.

Class 12 Physics Electromagnetic Induction Faraday's and Lenz's Law

Medium

The magnetic flux passing perpendicular to the plane of the coil and directed into the paper is varying according to the relation $\phi = 3t^2 + 2t + 3$,where $\phi$ is in milliwebers $(mWb)$ and $t$ is in seconds $(s)$. The magnitude of the $emf$ induced in the loop when $t = 2 \ s$ is ...... $mV$.

A
$31$
B
$19$
C
$14$
D
$6$

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Electromagnetic Induction

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Faraday's and Lenz's Law

In the following figure,the magnet is moved towards the coil with a speed $v$ and the induced $emf$ is $e$. If the magnet and the coil recede away from one another,each moving with speed $v$,the induced $emf$ in the coil will be: (Assume the separation in both cases is the same)

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If a coil of $40$ turns and area $4 \, cm^2$ is suddenly removed from a magnetic field,it is observed that a charge of $2 \times 10^{-4} \, C$ flows through the coil. If the resistance of the coil is $80 \, \Omega$,the magnetic flux density in $Wb \, m^{-2}$ is:

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The instantaneous magnetic flux associated with a closed loop of resistance $10 \ \Omega$ is given by $\phi = 2t^2 - 5t + 1$. The magnitude of the induced current at $t = 0.25 \ s$ will be . . . . . . . (in $A$)

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$A$ long solenoid with $15$ turns per $cm$ has a small loop of area $2.0 \,cm^2$ placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $2.0 \,A$ to $4.0 \,A$ in $0.1 \,s$, the induced emf in the loop while the current is changing is nearly [Take $\pi=3.14$].

DifficultMHT CET 2022

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$A$ square loop of wire,side length $10 \, cm$,is placed at an angle of $45^{\circ}$ with a magnetic field that changes uniformly from $0.1 \, T$ to zero in $0.7 \, s$. The induced current in the loop (its resistance is $1 \, \Omega$) is ..... $mA$.

Medium

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In the following figure,the magnet is moved towards the coil with a speed $v$ and the induced $emf$ is $e$. If the magnet and the coil recede away from one another,each moving with speed $v$,the induced $emf$ in the coil will be: (Assume the separation in both cases is the same)

If a coil of $40$ turns and area $4 \, cm^2$ is suddenly removed from a magnetic field,it is observed that a charge of $2 \times 10^{-4} \, C$ flows through the coil. If the resistance of the coil is $80 \, \Omega$,the magnetic flux density in $Wb \, m^{-2}$ is:

The instantaneous magnetic flux associated with a closed loop of resistance $10 \ \Omega$ is given by $\phi = 2t^2 - 5t + 1$. The magnitude of the induced current at $t = 0.25 \ s$ will be . . . . . . . (in $A$)

$A$ square loop of wire,side length $10 \, cm$,is placed at an angle of $45^{\circ}$ with a magnetic field that changes uniformly from $0.1 \, T$ to zero in $0.7 \, s$. The induced current in the loop (its resistance is $1 \, \Omega$) is ..... $mA$.

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