JEE Main 2025 — Electrostatics Question with Solution

We can use Gauss’s law to analyze the dimensions. Gauss’s law states that

$${\Phi }_E=\frac{q}{{ϵ}_0},$$

where

$${\Phi }_E$$ is the electric flux,

$$q$$ is the electric charge,

$${ϵ}_0$$ is the permittivity of free space.

To find the dimensions of $${ϵ}_0\frac{d{\Phi }_E}{dt}$$, follow these steps:

Differentiate Gauss’s law with respect to time:

$$\frac{d{\Phi }_E}{dt}=\frac{1}{{ϵ}_0}\frac{dq}{dt}.$$

Multiply the equation by $${ϵ}_0$$:

$${ϵ}_0\frac{d{\Phi }_E}{dt}=\frac{dq}{dt}.$$

Recognize that the time rate of change of charge, $$\frac{dq}{dt}$$, is by definition the electric current.

Thus, the dimensions of $${ϵ}_0\frac{d{\Phi }_E}{dt}$$ are those of electric current.

The correct answer is: Option C, electric current.