Question

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

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 written as J/C in place of V;

As $V=J/C$.

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

As, Joule is the product of force and displacement.

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

Prove that  1VM=1NC

$$\begin{gathered} 1\frac{V}{M}=1\frac{N.m}{C.m} \\ 1V/m=1N/C \end{gathered}$$