Q 11-01-241JEE MainJEE Main 2025 (2 Apr, Shift 2)Medium
Given a charge $q$, current $I$ and permeability of vacuum $\mu_0$. Which of the following quantities has the dimension of momentum?
Answer: (B) $q\mu_0I$
$[q] = AT$, $[I] = A$, and from $F = \dfrac{\mu_0 I_1I_2 l}{2\pi d}$, $[\mu_0] = MLT^{-2}A^{-2}$.
$$[q\mu_0I] = AT\cdot MLT^{-2}A^{-2}\cdot A = MLT^{-1}$$
This is the dimension of momentum. (The other options do not cancel the current: e.g. $[qI/\mu_0] = M^{-1}L^{-1}T^3A^4$.)
Solution by Sreeraj P, M.Sc Physics