Question

Show that the quantity ${\epsilon }_0\frac{{\text{dФ}}_e}{dt}$has units of current.

Short answer

Unit of${\epsilon }_0\frac{{\text{dФ}}_e}{dt}$is Ampere.

Step-by-step solution

Given Information:

We have been given an expression that we need to find the units of : ${\epsilon }_0\frac{{\text{dФ}}_e}{dt}$

Explanation:

According to:

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

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

Here F is Faraday; And its units correspond to as:

I = $\frac{Coulomb}{sec}$= Ampere (A).

Therefore the expression localid="1649877123640" ${\epsilon }_0\frac{{\text{dФ}}_e}{dt}$has units Ampere which is the same as that of current.