JEE Main · 2026 · 02 Apr 2026 · Shift 2 · 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

μ_{0}

. The mutual inductance between circular loop and square loop is

____

Answer: (D)

Solution

The magnetic field at the centre of a square loop of side

L

carrying current

I

B = \frac{2 2 μ _{0} I}{π L}

. Because

L ≫ R

, this field is essentially uniform over the small circular loop, so the flux linking it is

Φ = B π R^{2} = \frac{2 2 μ _{0} I}{π L} \times π R^{2} = \frac{2 2 μ _{0} R ^{2} I}{L}

. The mutual inductance is

M = \frac{Φ}{I} = \frac{2 2 μ _{0} R ^{2}}{L}

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Single correct option