Two concentric circular coils having radii r_ | vedclass

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

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

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

Two concentric circular coils having radii $r_1$ and $r_2$ $(r_2 \ll r_1)$ are placed co-axially with centres coinciding. The mutual inductance of the arrangement is (Both coils have single turn, $\mu_0$ = permeability of free space)

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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 coaxially with centers coinciding. Obtain the mutual inductance of the arrangement.

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