Two conducting circular loops of radii R _ 1 and R _ 2 are placed...

Two conducting circular loops of radii

{R}_{1}

and

{R}_{2}

are placed in the same plane with their centres coinciding. If

{R}_{1} ≫ {R}_{2}

, the mutual inductance

M

between them will be directly proportional to: Two conducting circular loops of radii R _ 1 and R _ 2 are placed in the same plane with their centres coinciding. If R

Two conducting circular loops of radii R _ 1 and R _ 2 are placed in the same plane with their centres coinciding. If R

Options

A $\dfrac{{R}_{1}}{{R}_{2}}$
B $\dfrac{{R}_{2}}{{R}_{1}}$
C ${R}_{2}^{2}{R}_{1}$
D ${R}_{1}^{2}{R}_{2}$

Correct answer

C. ${R}_{2}^{2}{R}_{1}$

Step-by-step solution

Two conducting circular loops of radii R _ 1 and R _ 2 are placed in the same plane with their centres coinciding. If R

$M = \dfrac{{ϕ}_{12}}{{I}_{1}} = \dfrac{{B}_{1}{A}_{2}}{{I}_{1}} = \dfrac{\left(\dfrac{{\mu}_{0}{I}_{1}}{2{R}_{1}}\right)\left(\pi{R}_{2}^{2}\right)}{{I}_{1}}$

$M = \dfrac{{\mu}_{0}\pi{R}_{2}^{2}}{2{R}_{1}}$

$∴ M ∝ {R}_{2}^{2}{R}_{1}$

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