7.5.3 Work Done on a Charge

• 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 = work done (J)
  • q = charge (C)
  • ∆V = change in potential difference (J C^-1)

• This 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

Step 1: Write down the known quantities

• • p.d. at R, V₁ = 286 V
  • p.d. at S, V₂ = 420 V
  • Charge, q = +3.0 nC = +3.0 × 10^-9 C

Step 2: Write down the work done equation

W = qΔV

Step 3: Substitute in the values into the equation

W = (3.0 × 10^-9) × (420 - 286) = 4.0 × 10^-7 J

• Equipotential lines (2D) and surfaces (3D) join together points that have the same electric potential
• These are always:
  • Perpendicular to the electric field lines in both radial and uniform fields
  • Represented by dotted lines (unlike field lines, which are solid lines with arrows)

• The potential gradient is defined by the equipotential lines

Equipotential lines around a radial field or uniform field are perpendicular to the electric field lines

• In a radial field (eg. a point charge), the equipotential lines:
  • Are concentric circles around the charge
  • Become further apart further away from the charge

• In a uniform field (eg. between charged parallel plates), the equipotential lines are:
  • Horizontal straight lines
  • Parallel
  • Equally spaced

• No work is done when moving along an equipotential line or surface
• Work is only done when moving between equipotential lines or surfaces
  • This means that an object travelling along an equipotential doesn't lose or gain energy and ΔV =  0