JEE Main 2025 Apr 4 Shift 2, Physics Q20: Units And Dimensions

JEE Main2025Apr 4, Shift 2Physics

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of $[M^{P} L^{Q} T^{R} A^{S}]$ . The value of $P$ and $Q$ are :

A
$- 1, 0$
B
$- 1, 1$
C
$1, - 1$
D
$0, - 1$

Solution

Electric dipole moment $p = q \cdot ℓ$ , so $[p] = [A T] [L] = L T A$ .

Magnetic dipole moment $M = I A$ , so $[M] = [A] [L^{2}] = L^{2} A$ .

Therefore

$[\frac{p}{M}] = \frac{L T A}{L ^{2} A} = L^{- 1} T = M^{0} L^{- 1} T^{1} A^{0}$ .

Comparing with $[M^{P} L^{Q} T^{R} A^{S}]$ : $P = 0, Q = - 1, R = 1, S = 0$ .

$∴ P = 0, Q = - 1$ .

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JEE Main 2025 Apr 4 Shift 2, Physics Q20: Units And Dimensions

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