JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Electromagnetic Induction

The dimension of mutual inductance is :

(A) $[ML^{2} T^{- 2} A^{- 1}]$
(B) $[ML^{2} T^{- 3} A^{- 1}]$
(C) $[M L^{2} T^{- 2} A^{- 2}]$ ✓ Correct
(D) $[M L^{2} T^{- 3} A^{- 2}]$

Answer: (C)

Solution

Mutual inductance

M

is defined by the relation

e_{2} = - M \frac{d i _{1}}{d t}

, where

e_{2}

is the induced emf and

i_{1}

is the current in the primary coil. Rearranging,

M = \frac{e _{2}}{d i _{1} / d t}

. The dimension of emf is

[e_{2}] = [W / q] = [M L^{2} T^{- 2}] / [A T] = [M L^{2} T^{- 3} A^{- 1}]

. The dimension of

d i_{1} / d t

[A T^{- 1}]

. Therefore,

[M] = \frac{[ M L ^{2} T ^{- 3} A ^{- 1} ]}{[ A T ^{- 1} ]} = [M L^{2} T^{- 2} A^{- 2}]

JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Single correct option

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