JEE Main 2026 Jan 22 Shift 2, Physics Q1: Faraday’s Law of Induction

JEE Main2026Jan 22, Shift 2Physics

If $ϵ, E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of $\frac{ϵ E}{t}$ will be :

Solution

From Gauss's law, $ϵ E$ has the dimensions of surface charge density: $ϵ E = \frac{q}{4 π r ^{2}}$ , i.e., $[ϵ E] = \frac{C}{m ^{2}}$ .

Dividing by time gives current per area:

$\frac{ϵ E}{t} = \frac{C / m ^{2}}{s} = \frac{A}{m ^{2}}$ .

This is exactly the displacement current density.

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