CIE A Level Physics (9702) exams from 2022

Revision Notes

18.2.3 Electric Potential Energy

Electric Potential Energy of Two Point Charges

  • The electric potential energy Ep at point in an electric field is defined as:

The work done in bringing a charge from infinity to that point

  • The electric potential energy of a pair of point charges Q1and Q2 is defined by:

Electric Potential Energy of Two Point Charges equation 1a

  • Where:
    • Ep = electric potential energy (J)
    • r = separation of the charges Q1 and Q2 (m)
    • ε0 = permittivity of free space (F m-1)
  • The potential energy equation is defined by the work done in moving point charge Q2 from infinity towards a point charge Q1.
  • The work done is equal to:

W = VQ

  • Where:
    • W = work done (J)
    • V = electric potential due to a point charge (V)
    • Q = Charge producing the potential (C)
  • This equation is relevant to calculate the work done due on a charge in a uniform field
  • Unlike the electric potential, the potential energy will always be positive
  • Recall that at infinity, V = 0 therefore Ep = 0
  • It is more useful to find the change in potential energy eg. as one charge moves away from another
  • The change in potential energy from a charge Q1 at a distance r1 from the centre of charge Q2 to a distance r2 is equal to:

Electric Potential Energy of Two Point Charges equation 2a

  • The change in electric potential ΔV is the same, without the charge Q2

Electric Potential Energy of Two Point Charges equation 3

  • Both equations are very similar to the change in gravitational potential between two points near a point mass

Worked example: Alpha particle

Electric_Potential_Energy_of_Two_Point_Charges_Worked_example_-_Alpha_Particle_Question, downloadable AS & A Level Physics revision notes

Step 1:           

Write down the known quantities

    • Distance, r = 4.7 × 10-15 m

The charge of one proton = +1.60 × 10-19 C

An alpha particle (helium nucleus) has 2 protons

    • Charge of alpha particle, Q1 = 2 × 1.60 × 10-19 = +3.2 × 10-19 C

The gold nucleus has 79 protons

    • Charge of gold nucleus, Q2 = 79 × 1.60 × 10-19 = +1.264 × 10-17 C

Step 2:           

Write down the equation for electric potential energy

Electric Potential Energy of Two Point Charges equation 1a

Step 3:           

Substitute values into the equation

Electric Potential Energy of Two Point Charges Worked Example equation

Exam Tip

When calculating electric potential energy, make sure you do not square the distance!

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