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Two concentric and coplanar coils have radii a and b (>> a) as shown in figure. Resistance of the inner coil is R. Current in the outer coil is increased from 0 to i, then the total charge circulating the inner coil is

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$\frac{μ_{0} i a^{2} π}{2 R b}$

$\frac{μ_{0} i b}{2 π R}$

$\frac{μ_{0} i a b}{2 a} \frac{π b^{2}}{R}$

$\frac{μ_{0} i a b}{2 R}$

answer is A.

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Detailed Solution

$△ q = \frac{△ ϕ}{R}$

$ϕ_{i} = 0$

$ϕ_{f} = (\frac{μ_{0}}{2} \frac{i}{b}) (π a^{2}) = \frac{μ_{0} i a^{2} π}{2 b}$

$∴ △ ϕ = ϕ_{f} - ϕ_{i} = \frac{μ_{0} i a^{2} π}{2 b}$

$S o, △ q = \frac{μ_{0} i a^{2} π}{2 R b}$

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