A coaxial circular coil having N turns, radius R is encircling a long solenoid [cross section area S and turns per unit length n]. The mutual inductance of the system is

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$μ_{0} n N S$

$\frac{μ_{0} n^{2} S}{N}$

$\frac{μ_{0} n^{2} S}{N + n}$

$\frac{μ_{0} n N S}{2}$

answer is A.

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Detailed Solution

Magnetic field inside the solenoid $= μ_{0} n I$
Flux through the circular coil encircling the solenoid $= μ_{0} n I S \cdot N = ϕ$
$M = \frac{ϕ}{I} = μ_{0} n S N$

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