(D) When we pass a current $I$ through the outer loop of radius $R$,the magnetic field at the centre is given by:$B_{\text{center}} = \frac{\mu_0 I}{2

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(D) When we pass a current $I$ through the outer loop of radius $R$,the magnetic field at the centre is given by:$B_{\text{center}} = \frac{\mu_0 I}{2 R}$Since $r \ll R$,the magnetic field $B$ is approximately uniform over the area of the smaller loop $A$.The magnetic flux $\phi$ associated with the smaller loop is:$\phi = B \cdot A = \left( \frac{\mu_0 I}{2 R} \right) \times (\pi r^2)$$\phi = \frac{\mu_0 I \pi r^2}{2 R}$The mutual inductance $M$ is defined as the ratio of the magnetic flux $\phi$ through the secondary coil to the current $I$ in the primary coil:$M = \frac{\phi}{I} = \frac{\mu_0 \pi r^2}{2 R}$

Class 12 Physics Electromagnetic Induction Mutual Induction

Easy

$O$ is the centre of two coplanar concentric circular conductors,$A$ and $B$,of radii $r$ and $R$ respectively as shown in the figure. Here $r \ll R$. The mutual inductance of the system of the conductors can be given by . . . . . . .

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A
$\frac{\mu_0 \pi r}{2 R}$
B
$\frac{\mu_0 R^2}{\pi r}$
C
$\frac{\mu_0 \pi R^2}{2 r}$
D
$\frac{\mu_0 \pi r^2}{2 R}$

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Electromagnetic Induction

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Mutual Induction

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Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1 >> R_2$,the mutual inductance $M$ between them will be directly proportional to

Medium

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Two coils $P$ and $Q$ are kept near each other. When no current flows through coil $P$ and current increases in coil $Q$ at the rate of $10 \ A/s$,the e.m.f. in coil $P$ is $15 \ mV$. When coil $Q$ carries no current and current of $1.8 \ A$ flows through coil $P$,the magnetic flux linked with coil $Q$ is (in $mWb$)

MediumMHT CET 2025

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Two coils have a mutual inductance $0.003 \ H$. The current changes in the first coil according to the equation $I = I_0 \sin \omega t$, where $I_0 = 8 \ A$ and $\omega = 100 \pi \ rad \ s^{-1}$. The maximum value of e.m.f. in the second coil is (in $\pi \ V$)

MediumMHT CET 2024

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Two coils have mutual inductance $0.002 \ H$. The current changes in the first coil according to the relation $i = i_0 \sin \omega t$,where $i_0 = 5 \ A$ and $\omega = 50 \pi \ rad/s$. The maximum value of $emf$ in the second coil is $\frac{\pi}{\alpha} \ V$. The value of $\alpha$ is . . . . . . .

DifficultJEE MAIN 2024

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$A$ primary coil and a secondary coil are placed close to each other. $A$ current, which changes at the rate of $25 \, A$ in a millisecond, is present in the primary coil. If the mutual inductance is $92 \times 10^{-6} \, H$, then the value of the induced emf in the secondary coil is:

EasyTS EAMCET 2012

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$O$ is the centre of two coplanar concentric circular conductors,$A$ and $B$,of radii $r$ and $R$ respectively as shown in the figure. Here $r \ll R$. The mutual inductance of the system of the conductors can be given by . . . . . . .

Similar Questions

Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1 >> R_2$,the mutual inductance $M$ between them will be directly proportional to

Two coils have a mutual inductance $0.003 \ H$. The current changes in the first coil according to the equation $I = I_0 \sin \omega t$, where $I_0 = 8 \ A$ and $\omega = 100 \pi \ rad \ s^{-1}$. The maximum value of e.m.f. in the second coil is (in $\pi \ V$)

Two coils have mutual inductance $0.002 \ H$. The current changes in the first coil according to the relation $i = i_0 \sin \omega t$,where $i_0 = 5 \ A$ and $\omega = 50 \pi \ rad/s$. The maximum value of $emf$ in the second coil is $\frac{\pi}{\alpha} \ V$. The value of $\alpha$ is . . . . . . .

$A$ primary coil and a secondary coil are placed close to each other. $A$ current, which changes at the rate of $25 \, A$ in a millisecond, is present in the primary coil. If the mutual inductance is $92 \times 10^{-6} \, H$, then the value of the induced emf in the secondary coil is:

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