16.1 Electric Potential Difference

16.1 Electric Potential Difference

The electric potential difference is the work done per unit charge in moving a charge between two points, and is expressed as:

The SI unit is the volt, where

It can be converted into other units such as kilovolts or millivolts by simple scaling. The relationship between electric potential difference and the electric field:

It is given by the fact that the electric field represents the rate of change of potential with distance, expressed as:

Where the negative sign indicates that the field points from higher to lower potential. In the case of a uniform electric field, this relation simplifies to:

Showing that the potential difference between two points is directly proportional to the electric field strength and the distance between them; thus, a stronger electric field causes a more rapid decrease in potential, providing a clear physical link between field intensity and voltage variation in space.

(Fig. 16.1)

Example 16.1

A $6$ volts battery is connected to two parallel copper plates separated by a distance of $0.3\,\mathrm{cm}$. Find the electric field intensity between them.

Solution

Potential difference between the plates $\Delta V = 6\,\mathrm{V}$

Distance between the plates $= \Delta d = 0.3\,\mathrm{cm} = 0.003\,\mathrm{m}$

Using, $E = \dfrac{\Delta V}{\Delta d}$

Putting the values, $E = \dfrac{6\,\mathrm{V}}{0.003\,\mathrm{m}} = 2000\,\mathrm{NC^{-1}}$

For your information

lightbulb

Although we have assumed that the points at infinity are at zero potential, yet the Earth is assumed to be at zero potential practically. Therefore, absolute value of the electric potential at a point is measured with respect to the Earth.