Question

Show that 1 V/m = 1 N/C.

Short answer

Proved that 1V/m=1N/C

Step-by-step solution

Definition of electric potential

The Electric potential (V) is considered as the electric potential energy for an unit of charge.

Hence, the Sl unit of this parameter is (J/C)

Application of Joule’s Formula for energy

As per consideration It can be write as J/C in place of V;

As $V=\frac{J}{C}$.

$\begin{array}{rcl}1\left(\frac{V}{m}\right)& =& 1\left(\frac{J}{C}\right)\times \left(\frac{1}{m}\right)\\ & & \\ 1\frac{V}{m}& =& 1\frac{J}{C.m}\end{array}$

As, Joule is the product of force and displacement.

Hence it can be written as, $J=N\times m$

Prove that 1VM=1NC

Now it is proved that

$\begin{array}{rcl}1\frac{v}{M}& =& 1\frac{N.m}{C.m}\\ 1V/m& =& 1N/C\end{array}$