   # Electric potential

The electric potential at a point in an electric field is defined as the work done in bringing a unit positive charge from infinity to that point.

An alternative definition is that it is the potential energy of a unit positive charge placed at that point with the zero being at infinity

The electric potential (VE) is given by the equation:

Electrostatic potential (VE) = (1/4peo)Q/d

The unit of electrostatic potential is the volt (V).

The variation of potential with distance from a charge Q is shown in Figure 1. If a charge q is in the field then its potential energy is given by :

Electrostatic potential energy = qVE = (1/4peo)qQ/d

and this is measured in joules.

When one positive charge moves away from another positive charge its potential energy is decreased but when a negative charge is moved away from a positive charge (e.g. electron and proton) its potential energy increases.

The variation of potential energy with distance is shown in Figure 2.

Example problems

1. Calculate the charge that produces a potential of 12 V at a distance of 0.1 nm in a vacuum.
Using:
VE= (1/4peo)Q/d   and therefore    Q = VEd/(1/4peo) = 10.8 C

2. Calculate the force on a charge of 3x10-5C placed in a field of strength 250 Vm-1.
Force = EQ = 3x10-5x250 = 7.5x10-3 N.

3. Calculate the potential energy of a charge of 10-9 C placed 0.1nm from a charge of 3 C.
Potential energy = (1/4peo)Qq/d = 9x10-9x10-9x3/10-10= 2.7 x10–7 J