JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Electromagnetic Induction

A small square look offside 'a' and one turn is placed inside a larger square loop of side b and one turn (

b ≫ a

). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop offside '

b

', then the coefficient of mutual inductance between the two loops is:

Answer: (D)

Solution

The field at the centre of the outer square loop of side

b

B = \frac{μ _{0} I}{4 π} \frac{8 2}{b}

. Since

b ≫ a

, this field is essentially uniform over the small inner loop, so the flux linked is

Φ = B a^{2} = \frac{μ _{0} I}{4 π} \frac{8 2 a ^{2}}{b}

. The mutual inductance is

M = \frac{Φ}{I} = \frac{μ _{0}}{4 π} 82 \frac{a ^{2}}{b} .

JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Single correct option