Question

A circular current loop of radius \( R \) is placed inside square loop of side length \( L \) (where \( L \gg R \)) such that they are co-planar and their centers coincide. The permeability of free space is \( \mu_0 \). The mutual inductance between the circular loop and square loop is _______.}

• A. \( \sqrt{2} \mu_0 \frac{L^2}{R} \)
• B. \( \sqrt{2} \mu_0 \frac{L^2}{R} \)
• C. \( \mu_0 \frac{L^2}{R} \)
• D. \( \frac{2 \mu_0 R^2}{L} \)

Answer 1

The Correct Option is A

Step 1: Formula for mutual inductance.
The mutual inductance between two co-planar loops (a circular loop and a square loop in this case) is given by: \[ M = \sqrt{2} \mu_0 \frac{L^2}{R} \] where \( \mu_0 \) is the permeability of free space, \( L \) is the side length of the square loop, and \( R \) is the radius of the circular loop.
Step 2: Conclusion.
Therefore, the mutual inductance between the circular loop and the square loop is \( \sqrt{2} \mu_0 \frac{L^2}{R} \).
Final Answer: (A) \( \sqrt{2} \mu_0 \frac{L^2}{R} \)