JEE Main 2025 Apr 2 Shift 2, Physics Q7: Units And Dimensions

JEE Main2025Apr 2, Shift 2Physics

Given a charge $q$ , current $I$ and permeability of vacuum $μ_{0}$ . Which of the following quantity has the dimension of momentum ?

Solution

Use dimensional analysis with $[q] = A T$ , $[I] = A$ and $[μ_{0}] = M L T^{- 2} A^{- 2}$ .

Set $[q^{x} μ_{0}^{y} I^{z}] = M L T^{- 1}$ , the dimension of momentum.

Combining: $[q^{x} μ_{0}^{y} I^{z}] = (A T)^{x} (M L T^{- 2} A^{- 2})^{y} (A)^{z} = M^{y} L^{y} T^{x - 2 y} A^{x - 2 y + z}$ .

Matching to $M L T^{- 1}$ (with no $A$ ): $y = 1$ , $y = 1$ (already), $x - 2 y = - 1 \Rightarrow x = 1$ , and $x - 2 y + z = 0 \Rightarrow z = 1$ .

So the required combination is $q μ_{0} I$ .

Concept behind this question

Concept-wise practice with instant solutions on Fundamenthol.