Electric Potential Energy Equation (HL) (HL IB Physics)

• When a mass with charge moves through an electric field, work is done
• The work done in moving a charge q is given by:

∆W = q∆V

• Where:
  • ∆W = change in work done (J)
  • q = charge (C)
  • ∆V = change in electric potential (J C^-1)

• This change in work done is equal to the change in electric potential energy (E.P.E)
  • When V = 0, then the E.P.E = 0

• The change in E.P.E, or work done, for a point charge q at a distance r₁ from the centre of a larger charge Q, to a distance of r₂ further away can be written as:

• Where:
  • Q = charge that is producing the electric field (C)
  • q = charge that is moving in the electric field (C)
  • r₁ = first distance of q from the centre of Q (m)
  • r₂ = second distance of q from the centre of Q (m)

Work is done when moving a point charge away from another charge

• Work is done when a positive charge in an electric field moves against the electric field lines or when a negative charge moves with the electric field lines

Electrical Potential Difference

• Two points at different distances from a charge will have different electric potentials
  • This is because the electric potential increases with distance from a negative charge and decreases with distance from a positive charge

• Therefore, there will be an electric potential difference between the two points
  • This is represented by the symbol ΔV

• ΔV is normally given as the equation

ΔV = V_f – V_i

• Where:
  • V_f = final electric potential (J C^-1)
  • V_i = initial electric potential (J C^-1)

Electrical Potential Energy

• 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 Q₁ and 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