7.3.3 Electric potential

Definition

The formula for electric potential in a radial field around a point charge $Q$ is:

Where:

$$V = \frac{1}{4 \pi \epsilon_0} \frac{Q}{r}$$

• $\epsilon_0$ is the permittivity of free space
• $Q$ is the charge creating the field
• $r$ is the distance from the charge.

Positive or Negative Potential:

The sign of the electric potential depends on the charge:

• Positive charge $Q$ results in positive potential and a repulsive force.

• Negative charge $Q$ results in negative potential and an attractive force.

Electric Field Strength and Potential

The electric field strength ($E$) at a particular point is the gradient of the electric potential ($V$) against the distance ($r$):

$$E = -\frac{\Delta V}{\Delta r}$$

This can be determined by taking the gradient (slope) of a tangent to a graph of potential $V$ against distance $r$.

Electric Potential Difference $\Delta V$

The electric potential difference $(\Delta V)$ represents the energy needed to move a unit charge between two points in an electric field. The work done ( $\Delta W$) to move a charge $Q$ across a potential difference $\Delta V$ is given by:

$$\Delta W = Q \Delta V$$

Equipotential Surfaces

Equipotential surfaces are surfaces where all points have the same electric potential. Therefore:

• No work is done when a charge moves along an equipotential surface, as there is no potential difference.
• In a uniform field, equipotential surfaces are planes parallel to the plates, while around a point charge they form concentric circles.

Finding Electric Potential Difference from a Field Strength Graph

By plotting electric field strength ($E$) against distance ($r$), the area under the curve between two points on this graph gives the electric potential difference ( $\Delta V$) between those points.