Key Equations

Electric Fields & Potential — AQA A-Level Physics

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Coulomb's law
$$F = \frac{Q_1 Q_2}{4\pi\varepsilon_0 r^2}$$
  • Where:
    • $F$ = electrostatic force (N)
    • $Q_1, Q_2$ = charges (C)
    • $r$ = separation (m)
    • $varepsilon_0$ = permittivity of free space (F m^-1)
Positive F = repulsion (like charges). Negative F = attraction (unlike charges). r is centre-to-centre.
Electric potential energy of two point charges
$$E_p = \frac{Q_1 Q_2}{4\pi\varepsilon_0 r}$$
  • Where:
    • $E_p$ = electric potential energy (J)
    • $Q_1, Q_2$ = charges (C)
    • $r$ = separation (m)
Positive for like charges (repulsion). Negative for unlike charges (attraction). E_p = 0 at infinity.
Field strength from potential gradient
$$E = -\frac{\Delta V}{\Delta r}$$
  • Where:
    • $E$ = electric field strength (V m^-1)
    • $DeltaV$ = potential difference (V)
    • $Deltar$ = displacement in field direction (m)
Negative sign: field points towards lower potential. Gradient of V-r graph = E.
Electric field strength (general)
$$E = \frac{F}{Q}$$
  • Where:
    • $E$ = electric field strength (N C^-1)
    • $F$ = force (N)
    • $Q$ = charge (C)
Defines E. Works for any field shape.
Uniform field between parallel plates
$$E = \frac{V}{d}$$
  • Where:
    • $E$ = electric field strength (V m^-1)
    • $V$ = potential difference (V)
    • $d$ = plate separation (m)
Only for uniform fields between parallel plates. Not for point charges.
Radial field strength (point charge)
$$E = \frac{Q}{4\pi\varepsilon_0 r^2}$$
  • Where:
    • $E$ = electric field strength (N C^-1)
    • $Q$ = source charge (C)
    • $r$ = distance from centre (m)
Follows an inverse square law. E-r graph is a 1/\(r^{2}\) curve.
Electric potential (point charge)
$$V = \frac{Q}{4\pi\varepsilon_0 r}$$
  • Where:
    • $V$ = electric potential (V)
    • $Q$ = source charge (C)
    • $r$ = distance from centre (m)
Positive Q gives positive V. Negative Q gives negative V. V = 0 at infinity.
Work done on a charge
$$\Delta W = q \Delta V$$
  • Where:
    • $DeltaW$ = work done (J)
    • $q$ = charge being moved (C)
    • $DeltaV$ = potential difference (V)
q is the charge being moved, not the charge producing the field.
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