JEE Mains · Physics · STD 12 -6. Electromagnetic induction
A circular current loop of radius \(R\) is placed inside square loop of side length \(L\) \((L >> R)\) such that they are co-planar and their centers coincide. The permeability of free space is \(\mu_0\). The mutual inductance between circular loop and square loop is _______.
- A \(2\sqrt{2} \, \dfrac{\mu_0 L^2}{R}\)
- B \(\sqrt{2} \, \dfrac{\mu_0 L^2}{R}\)
- C \(\sqrt{2} \, \dfrac{\mu_0 R^2}{L}\)
- D \(2\sqrt{2} \, \dfrac{\mu_0 R^2}{L}\)
Answer & Solution
Correct Answer
(D) \(2\sqrt{2} \, \dfrac{\mu_0 R^2}{L}\)
Step-by-step Solution
Detailed explanation
Using the reciprocity theorem, assume a current \(I\) flows through the larger square loop and compute the flux through the smaller circular loop. The mutual inductance is given by \(M = \dfrac{\Phi}{I}\). Magnetic field at the centre of the square loop: For a square of side…
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