Mutual Inductance of Two Co-axial Coils – Rankers Physics
Topic: Electromagnetic Induction
Subtopic: Mutual Induction

Mutual Inductance of Two Co-axial Coils

Two circular coils one of small radius \(r\) and other of larger radius \(R\) (\(r \ll R\)) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is
\(\frac{\mu_0 \pi R^2}{r}\)
\(\frac{\mu_0 \pi r^2}{2R}\)
\(\frac{\mu_0 \pi r R}{r + R}\)
\(\frac{2 \mu_0 \pi r^2}{R}\)

Solution:

The magnetic field at the center of the outer coil of radius \(R\) carrying current \(I\) is \(B = \frac{\mu_0 I}{2R}\). The flux through the inner coil of radius \(r\) is \(\Phi = B \cdot (\pi r^2) = \frac{\mu_0 \pi r^2 I}{2R}\). Thus, \(M = \frac{\Phi}{I} = \frac{\mu_0 \pi r^2}{2R}\).

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