A circular current loop of radius R is placed inside square loop of side length such that they are co-planar and their centers coincide

Question

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 ________. [2026]

Smart Achievers · Accepted Answer

(4)

$B at center of square loop =$

$= 4 \times \frac{μ_{0} I}{4 π \frac{L}{2}} (\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}})$

$\Rightarrow \frac{2 μ_{0} I}{π L} \times \frac{2}{\sqrt{2}}$

$= \frac{2 \sqrt{2} μ_{0} I}{π L}$

$ϕ = \frac{2 \sqrt{2} μ_{0} I}{π L} \times π R^{2}$

$M = \frac{ϕ}{I} = \frac{2 \sqrt{2} μ_{0} R^{2}}{L}$

Solution

Q.
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 ________. [2026]

1 $2 \sqrt{2} \frac{μ_{0} L^{2}}{R}$

2 $\sqrt{2} \frac{μ_{0} L^{2}}{R}$

3 $\sqrt{2} \frac{μ_{0} R^{2}}{L}$

4 $2 \sqrt{2} \frac{μ_{0} R^{2}}{L}$

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Solution

Q. 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 μ0. The mutual inductance between circular loop and square loop is ________. [2026]

1 22μ0L2R

2 2μ0L2R

3 2μ0R2L

4 22μ0R2L