Question

Write down the relationship between potential gradient and intensity of electric field. What is the S.I. unit of potential gradient?

Answer 1

Let us consider two closely spaced equipotential surfaces A and B as shown in figure. Let the potential of A be V_A​ = V and potential of B be VB​= V−dV is decrease in potential in the direction of electric field \(\vec E\) normal to A and B.

Let dr be the perpendicular distance between the two equipotential surfaces. when a unit positive charge is moved along this perpendicular from the surface B to surface A against the electric field, the work done in this process is 

\(W _{BA} = - \vec E (dr)\)

This work done equals the potential difference V_A​−V_B​ 

∴ W_{BA ​}= V_A​−V_B​ 

= V − (V−dV)

= dV 

\(\therefore - \vec E.dr = dV\)

or, \(\vec E = - \frac {dV}{dr}\) = negative of potential gradient

SI unit of the potential gradient is volt/metre.