﻿ Potential due to a Point Charge | Electrostatic Potential and Capacitance - Zigya

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# Electrostatic Potential and Capacitance

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## Potential due to a Point Charge

Consider a point charge Q at origin O. Let P be a point at a distance r from it.

Take Q to be positive charge.  For Q > 0, the work done against the repulsive force on the test charge is positive.

If the charge Q is negative, the potential is also negative as the test charge will have a force of attraction.

The electrostatic potential is inversely proportional to r and electrostatic field is inversely proportional to the square of r.

At some intermediate point P′ on the path, the electrostatic force on a unit positive charge is

where ˆr′ is the unit vector along OP′.

Work done against this force from r′ to r′ + ∆r′ is

Total potential at P due to the charge Q