# Relation between Field and Potential

## Relation between Field and Potential

Electric Field is a force produce by a charge near its surroundings. This force is exerted on other charges when brought in the vicinity of this field. The SI unit of Electric field is N/C. Electric field due to a charge at a point is the force that a unit positive charge would experience if placed at that point.

Inside a field, the amount of work need to move a unit positive charge from one initial point to any specified point without producing any acceleration is known as Electrostatic Potential or Electric Potential or Electric Field Potential.

Consider two closely spaced equipotential surfaces A and B with potential values V and (V + δV), where δV is the change in V in the direction of the electric field E. Let P be a point on the surface B, δl is the perpendicular distance of the surface A from P. Imagine that 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 |E| δl.

This work equals the potential difference VA – VB. Thus,

|E| δl = V – (V + δV) = – δV

i.e. $$|E|=-\frac{\delta V}{\delta l}$$.

Since δV is negative, δV = – |δV| we can rewrite the above equation as:

$$|E|=-\frac{\delta V}{\delta l}=+\frac{|\delta V|}{\delta l}$$.

We thus arrive at two important conclusions concerning the relation between electric field and potential:

1. Electric Field is in the direction in which the potential decreases steepest.

2. Its magnitude is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at the point.