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# Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to:

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Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to:

(1) $$\frac{R_1}{R_2}$$

(2) $$\frac{R_2}{R_1}$$

(3) $$\frac{R_1^2}{R_2}$$

(4) $$\frac{R_2^2}{R_1}$$

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Correct answer: (4) $$\frac{R_2^2}{R_1}$$

Explanation:

M = $$\frac{ϕ_{12}}{I_1}$$ = $$\frac{B_1A_2}{I_1}$$

= $$\frac{\frac{(\mu_0I_1}{2R_1})(\pi R_2^2)}{I_1}$$

= $$\frac{\mu_0 \pi R_2^2}{2R_1}$$

M ∝ $$\frac{R_2^2}{R_1}$$

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