Electric Potential Energy (DP IB Physics: HL): Revision Note

Electric Potential Energy

• In a system of two or more charges, electric potential energy is stored due to the electric forces between them

• The electric potential energy of a system is defined as

The work done in bringing all the charges in a system to their positions from infinity

• Electric potential energy can be positive or negative, depending on the charges involved 

  • This is different from gravitational potential energy, which always has a negative value

• Electric potential energy has a positive value when:

  • the electric force is repulsive i.e. between two similar charges

  • energy is released as charges become separated

• Electric potential energy has a negative value when:

  • the electric force is attractive i.e. between two opposite charges

  • energy must be supplied to separate the charges

• A graph of potential energy E_p against distance r can be drawn for two like charges and two opposite charges

• The gradient of the graph at any particular point is equal to the electric force F at that point

Graph of electric potential energy against distance

The electric potential energy of two similar charges decreases with distance and increases for two opposite charges

Electric Potential Energy Equation

• The electric potential energy of two point charges is given by:

$E_p=k\frac{q_1{q}_2}{r}$

• Where:

  • E_p = electric potential energy (J)

  • q₁, q₂ = magnitudes of the charges (C)

  • r = distance between the centres of the two charges (m)

  • k = Coulomb constant (N m² C^–2)

• Similar to electric potential, values of electric potential energy depend on the signs of q1 and q2

  • By definition, potential V = 0 at infinity, therefore E_p = 0 at infinity

• The electric potential energy of two charges separated by a distance R can also be determined from the area under a force-distance graph

  • However, determining this area for distances between R and infinity is difficult, so it is much simpler to use the equation above

Determining area under an electric force-distance graph

The area under the force-distance graph represents the electric potential energy of two similar point charges separated by R

Change in Electric Potential Energy

• There is a change in electric potential energy when one charge moves away from another

  • This is because work must be done on the field to bring similar charges together, or to separate opposite charges

  • Conversely, work is done by the field to separate similar charges, or to bring opposite charges together

• When a charge q₂ moves away from a charge q₁, the change in electric potential energy is equal to:

$∆E_{\mathrm{p}}=k{q}_1{q}_2(\frac{1}{r_1}-\frac{1}{r_2})$

• Where:

  • r₁ = initial separation between charges (m)

  • r₂ = final separation between charges (m)

There is a change in electric potential energy when a point charge moves away from another charge

• The change in electric potential energy between two charges is analogous to the change in gravitational potential energy between two masses

Comparing gravitational and electric potential energy

When a small mass is lifted on Earth, there is an increase in gravitational potential energy. This is similar to the increase in electric potential energy when a negative charge moves away from a positive charge

Determining work done from a force-distance graph

• The work done in moving a charge can also be determined from the area under a force-distance graph

• This is equivalent to the change in electric potential energy of a moving charge

The area under a force-distance graph represents the change in electric potential energy, or the work done in moving the charge