O is the centre of two coplanar concentric ci | vedclass

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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_{	ext{center}} = \frac{\mu_0 I}{2

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$\frac{\mu_0 \pi r^2}{2 R}$

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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:$B_{	ext{center}} = \frac{\mu_0 I}{2 R}$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} ight) 	imes (\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:$M = \frac{\phi}{I} = \frac{\mu_0 \pi r^2}{2 R}$

$O$ 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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