Two concentric circular coils having radii r_ | vedclass

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Question

(D) If a current $I_{1}$ flows in the outer coil of radius $r_{1}$,the magnetic field at the center is given by $B_{1} = \frac{\mu_{0} I_{1}}{2 r_{1}}

Vedclass · Accepted Answer

$\frac{\mu_{0} \pi r_{2}^{2}}{2 r_{1}}$

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(D) If a current $I_{1}$ flows in the outer coil of radius $r_{1}$,the magnetic field at the center is given by $B_{1} = \frac{\mu_{0} I_{1}}{2 r_{1}}$.Since $r_{2} \ll r_{1}$,we assume the magnetic field $B_{1}$ is uniform over the area of the smaller coil.The magnetic flux $\phi_{2}$ passing through the inner coil of radius $r_{2}$ is $\phi_{2} = B_{1} 	imes A_{2} = B_{1} 	imes \pi r_{2}^{2}$.Substituting the value of $B_{1}$,we get $\phi_{2} = \left( \frac{\mu_{0} I_{1}}{2 r_{1}} ight) 	imes \pi r_{2}^{2}$.The mutual inductance $M$ is defined as $M = \frac{\phi_{2}}{I_{1}}$.Therefore,$M = \frac{\mu_{0} \pi r_{2}^{2}}{2 r_{1}}$.

Two concentric circular coils having radii $r_{1}$ and $r_{2}$ $(r_{2} \ll r_{1})$ are placed coaxially with centers coinciding. The mutual inductance of the arrangement is (Both coils have a single turn) ($\mu_{0} =$ permeability of free space).

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