(C) The magnetic field at the center of a large circular coil of radius $r_2$ carrying current $I$ is given by $B = \frac{\mu_0 I}{2 r_2}$.Since $r_1

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$\frac{\mu_0 \pi r_1^2}{2 r_2}$

(C) The magnetic field at the center of a large circular coil of radius $r_2$ carrying current $I$ is given by $B = \frac{\mu_0 I}{2 r_2}$.Since $r_1 \ll r_2$,we assume the magnetic field $B$ is uniform over the area of the smaller coil of radius $r_1$.The magnetic flux $\phi$ linked with the smaller coil is $\phi = B \cdot A = \left(\frac{\mu_0 I}{2 r_2}\right) \cdot (\pi r_1^2)$.The mutual inductance $M$ is defined as $M = \frac{\phi}{I}$.Substituting the expression for $\phi$,we get $M = \frac{\mu_0 \pi r_1^2}{2 r_2}$.

Class 12 Physics Electromagnetic Induction Mutual Induction

Medium

Two circular coils of radii $r_1$ and $r_2$ $(r_1 \ll r_2)$ are placed coaxially with their centers coinciding. The mutual inductance of the arrangement is

TS EAMCET 2024 All TS EAMCET

A
$\frac{\mu_0 \pi r_2^2}{2 r_1}$
B
$\frac{\mu_0 \pi r_1 r_2}{2(r_1+r_2)}$
C
$\frac{\mu_0 \pi r_1^2}{2 r_2}$
D
$\frac{\mu_0 \pi(r_1+r_2)}{2 r_1 r_2}$

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Electromagnetic Induction

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DifficultKVPY 2019

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Two concentric circular coils, one of small radius $r_1$ and the other of large radius $r_2$, such that $r_1 \ll r_2$, are placed co-axially with their centres coinciding. The mutual inductance $M$ of the arrangement is proportional to . . . . . . .

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Two circular coils of radii $r_1$ and $r_2$ $(r_1 \ll r_2)$ are placed coaxially with their centers coinciding. The mutual inductance of the arrangement is

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The coefficient of mutual induction is $2 \text{ H}$ and the induced e.m.f. across the secondary is $2 \text{ kV}$. The current in the primary is reduced from $6 \text{ A}$ to $3 \text{ A}$. The time required for the change of current is:

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