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

Question

Accepted Answer

$\dfrac{R_2^2}{R_1}$. When one loop is much smaller than the other, the flux through the smaller loop is approximately the magnetic field due to the larger loop times the area of the smaller loop. Since the field at the center of a circular loop varies as $1/R_1$ and the area of the smaller loop varies as $R_2^2$, we get $M\propto R_2^2/R_1$.

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

Solution

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