• The electric potential energy E_p 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:

• Where:
  • E_p = 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 E_p = 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:

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

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

Worked Example

• • 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

Exam Tip