# 7.5.3 Work Done on a Charge

### 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 = qV

• Where:
• W = change in work done (J)
• q = charge (C)
• Vchange 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)
• r1first distance of q from the centre of Q (m)
• r2 = second distance of q from the centre of Q (m)

• 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

#### Worked Example

The potentials at points R and S due to the +7.0 nC charge are 675 V and 850 V respectively. Calculate how much work is done when a +3.0 nC charge is moved from R to S.

Step 1: Write down the known quantities

• p.d. at R, V1 = 675 V
• p.d. at S, V2 = 850 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) × (850 – 675) = 5.3 × 10-7 J

#### Exam Tip

Remember that q in the work done equation is the charge that is being moved, whilst Q is the charge which is producing the potential. Make sure not to get these two mixed up, as both could be given in the question (like the worked example) and you will be expected to choose the correct one

### Electrostatic Equipotential Surfaces

• 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 ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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