Electric Potential (AQA A Level Physics): Revision Note

Electric potential

• The electric potential of a point charge is defined as:

The work done per unit charge in taking a small positive test charge from infinity to a defined point

• Electric potential is measured in J C⁻¹ or V

• It is a scalar quantity but has a positive or negative sign to indicate the sign of the charge

  • In a similar way to gravitational potential, electric potential also has a value of zero at infinity

• The electric potential at a point depends on:

  • the magnitude of the point charge

  • the distance between the charge and the point

Electric potential for a positive charge

• Around an isolated positive charge, electric potential: 

  • has a positive value

  • increases when a test charge moves closer

  • decreases when a test charge moves away

Electric potential for a negative charge

• Around an isolated negative charge, electric potential: 

  • has a negative value

  • decreases when a test charge moves closer

  • increases when a test charge moves away

Electric potential in radial field

• The electric potential around a point charge can be calculated using: 

$V=\frac{Q}{4\mathrm{\pi }{\epsilon }_{0}r}$

• Where:

  • $V$ = electric potential (V)

  • $Q$ = magnitude of the charge producing the potential (C)

  • $r$ = distance from the centre of the point charge (m)

  • ${\epsilon }_0$ = permittivity of free space (F m⁻¹)

• For a positive (+) charge:

  • potential $V$ increases as the separation $r$ decreases

  • energy must be supplied to a positive test charge to overcome the repulsive force

• For a negative (−) charge:

  • potential $V$ increases as the separation $r$ increases

  • energy is released as a positive test charge moves in the direction of the attraction force

• The electric potential has an inversely proportional relationship with distance

• Unlike gravitational potential which is always negative, the sign of the charge corresponds to the sign of the electric potential

• Note: this equation also applies to a conducting sphere. The charge on the sphere is treated as if it is concentrated at the centre of the sphere, i.e. like a point charge

Combining electric potentials

• To find the potential at a point caused by multiple charges, each potential can be combined by addition

• For example, the combined potential of two point charges at a point is:

$V=\frac{Q_1}{4\mathrm{\pi }{\epsilon }_0{r}_1}+\frac{Q_2}{4\mathrm{\pi }{\epsilon }_0{r}_2}$

• Where:

  • $Q_1$, $Q_2$ = magnitude of the charges (C)

  • $r_1$, $r_2$ = distance between each charge and the point (m)