Two closely spaced equipotential surfaces A and B with potentials V and `V + deltaV` (where SV is the change in V) are kept 8l distance apart as shown in the Fig. Deduce the relation between the electric field and the potential gradient between them. Write the two important conclusions concerning the relation between the electric field and the electric potential.

Explanation

Consider two closely spaced equipotential surfaces A and B, having uniform potentials V and V + `deltaV` in the direction of the electric field E. Let `deltal` be the perpendicular distance of the surface A from a point P on surface B.
If we consider that a unit +ve charge is moved along this perpendicular from surface B to surface A against the electric field then work done
`deltaW = E deltaI`
By definition the work done equals the potential difference
`(V_A - V_B) = V- (V + deltaV) = deltaV`
`rArr E delta I = - deltaV or E = - (deltaV)/(deltaI) (or -(dV)/(dl))`
For two important conclusions.