Question

Show that the quantity ${ϵ}_0\left(d{\Phi }_{\mathrm{e}}/dt\right)$has units of current.

Short answer

The Displacement Current

or

${\epsilon }_0\frac{EA}{dt}unit\text{is equal to current unit.}$

Step-by-step solution

Given information:

${\epsilon }_0\frac{d{\varphi }_e}{dt}={\epsilon }_0\frac{EA}{dt}$

Simplify

$=\frac{F}{m}\frac{\left(\frac{V}{m}\right)m^2}{s}$

$=\frac{C}{V}\left(\frac{V}{s}\right)$

As ,we know that Faraday has unit $F=\frac{\text{Columb}}{\text{volt}}$

V is the voltage and sec is the unit of time

$I=\frac{C}{s}$

$=\frac{\text{Columb}}{\sec }$

$=A\left(\text{Amphere}\right)$

so, is is clear that${\epsilon }_0\frac{EA}{dt}$unit is equal to current unit.