Chapter-2|Electrostatic Potential and Capacitance| NCERT 12th Physics:
Relation Between Electric Field and Electric Potential:
We consider the electric field due to charge +q located at the origin O. Let A and B be two adjacent point separated by distance dr. The two points A and B are so close that the electric field E between them remains almost constant. Let V and V+dv be the potential difference at two points.
The external force required to move the test charge q₀ against the electric field E is
The work done to move the test charge from A to B is
The quantity dV/dr is the rate of change of potential with distance and is called potential gradient.
Thus the electric field at any point is equal to the negative of the potential gradient at that point. The negative sign shows that the direction of E is in the direction of decreasing potential.