A-Level Physics: Electric Fields and Capacitance

Electric fields and capacitance pair the second inverse-square field with the exam's favourite exponential system — the RC circuit. This quiz covers both, with the multi-quantity capacitor problems that reward systematic working.

The field questions run the point-charge toolkit with real values: Coulomb's law for the force between two microcoulomb charges (0.80 N), the potential at a distance from a point charge, force on a charge in a uniform field, and the acceleration of an electron between plates — the charge-to-mass calculation that lands near 10¹⁴ m/s² and tests powers-of-ten discipline as much as physics.

The capacitance questions centre on a parallel-plate problem examined as a statement set: capacitance from plate area and separation, energy stored, with distractors for the field strength between the plates and the charge stored, both of which must be recomputed rather than guessed. Further questions recover capacitance from stored energy, combine capacitors in series through the reciprocal rule, and work the charge-sharing problem — a charged capacitor reconnected across an uncharged one, solved by conserving charge and dividing by the combined capacitance.

The RC-circuit questions close the set: which factors define the time constant (resistance and capacitance only), and the qualitative shape of charging through a resistor — current decaying exponentially as the capacitor's pd rises.

Every constant and value is given in the question, matching the data-booklet exam format, and each explanation traces the complete numeric chain with units carried throughout.

  • Apply Coulomb's law and point-charge potential with given values
  • Compute forces and accelerations of charges in uniform fields
  • Work parallel-plate capacitance, charge and stored energy consistently
  • Combine capacitors in series and solve charge-sharing problems
  • Reason about RC charging and discharging and the time constant

Topic scope follows the A-level physics content — as organised, for example, in sections 3.7.3–3.7.4 (Electric fields; Capacitance) of the AQA A-level Physics (7408) specification: Coulomb's law, field strength and potential, parallel plates, capacitor energy, and charge/discharge through a resistor.

Sample question

A parallel plate capacitor: two horizontal plates of area A a distance d apart, connected to a source of potential difference V.

A parallel plate capacitor has plates of area $0.050 \text{ m}^2$ separated by a distance of $2.0 \text{ mm}$ in a vacuum. If the potential difference across the plates is $100 \text{ V}$, which of the following statements are correct? (Permittivity of free space $\epsilon_0 = 8.85 \times 10^{-12} \text{ F m}^{-1}$)

See the answer

The capacitance is approximately $2.21 \times 10^{-10} \text{ F}$, The energy stored is approximately $1.11 \times 10^{-6} \text{ J}$

Capacitance $C = \frac{\epsilon_0 A}{d} = \frac{8.85 \times 10^{-12} \cdot 0.050}{0.002} = 2.21 \times 10^{-10} \text{ F}$. Energy stored $W = \frac{1}{2}CV^2 = 0.5 \cdot 2.21 \times 10^{-10} \cdot 100^2 = 1.11 \times 10^{-6} \text{ J}$. The electric field strength $E = \frac{V}{d} = \frac{100}{0.002} = 5.0 \times 10^4 \text{ V m}^{-1}$, not $200 \text{ V m}^{-1}$. The charge $Q = CV = 2.21 \times 10^{-8} \text{ C}$, not $1.11 \times 10^{-7} \text{ C}$.

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