Mutual Inductance of Concentric Coils – Rankers Physics

Mutual Induction: Practice Problem & Solution

A square coil of side length \(l\) is placed at centre of a large circular coil of radius \(R\), where \(R \gg l\) and coils are in same plane. The coefficient of mutual inductance of the coils is
\(\frac{\mu_0 l^2}{2R}\)
\(\frac{\mu_0 l}{2R}\)
\(\frac{\mu_0 l^2}{2\pi R}\)
\(\frac{\mu_0 l}{2\pi R}\)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Mutual Induction. Understanding the underlying formula is key to arriving at the correct answer below:

Let a current \(I\) flow through the large circular coil, producing a magnetic field \(B = \frac{mu_0 I}{2R}\) at its center. The flux through the small square coil is \(\Phi = B'A = \left(\frac{\mu_0 I}{2R}\right) l^2\). Therefore, the mutual inductance is \(M = \frac{\Phi}{I} = \frac{\mu_0 l^2}{2R}\).

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