JEE Main 2026 — Units and Dimensions Question with Solution

We need to find the unit of $\frac{ϵE}{t}$.
From Maxwell's equations, the displacement current density is given by $J_d=ϵ\frac{\partial E}{\partial t}$.
The term $\frac{ϵE}{t}$ has the same dimensions as displacement current density $J_d$.
Current density $J$ is defined as current per unit area, $J=\frac{I}{A}$.
The SI unit of current $I$ is Ampere (A) and the SI unit of area $A$ is $m^2$.
Therefore, the unit of current density is $A/m^2$.
Alternatively, using dimensions:
$[ϵ]=M^{-1}{L}^{-3}{T}^4{A}^2$
$[E]=ML{T}^{-3}{A}^{-1}$
$[t]=T$
Dimension of $\frac{ϵE}{t}=\frac{(M^{-1}{L}^{-3}{T}^4{A}^2)(ML{T}^{-3}{A}^{-1})}{T}=L^{-2}A$.
This corresponds to the unit $A/m^2$.