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Electric fields between parallel plates

Always Question One, every year on record — and until now this page had no dedicated section for it at all, despite it being roughly a third of every paper.

The three formulas that chain together

  • Field strength: E = V/d — the voltage across the plates divided by the separation between them.
  • Force on a charge: F = qE (equivalently F = Eq) — the force felt by a charge sitting in that field.
  • Energy: E_p = qV — the electric potential energy gained or lost by a charge q moving through the full potential difference V.
  • Field lines point from the POSITIVE plate to the NEGATIVE plate; a positive charge feels a force in the direction of the field, a negative charge (like an electron) feels a force AGAINST it.
Worked example Chaining all three formulas for an electron Parallel plates are 0.050 m apart with 12 V across them. An electron (charge 1.60×10⁻¹⁹ C, mass 9.11×10⁻³¹ kg) starts at rest at the negative plate. Find its speed when it reaches the positive plate. Field strength: E = V/d = 12 / 0.050 = 240 V m⁻¹. Force on the electron: F = qE = 1.60×10⁻¹⁹ × 240 = 3.84×10⁻¹⁷ N. Energy gained crossing the full gap: Eₚ = qV = 1.60×10⁻¹⁹ × 12 = 1.92×10⁻¹⁸ J. That energy becomes kinetic energy: ½mv² = 1.92×10⁻¹⁸, so v² = 2×1.92×10⁻¹⁸ / 9.11×10⁻³¹. v = √(4.21×10¹²) ≈ 2.05×10⁶ m s⁻¹. ✓ v ≈ 2.05 × 10⁶ m s⁻¹ — note the energy method (Eₚ = qV → KE) is faster here than working through force and acceleration separately.

When a charge is held stationary between the plates

  • A charge is stationary when the ELECTRIC force (qE, from the plates) exactly balances the GRAVITATIONAL force (mg, downward) — this is the classic Millikan oil-drop setup.
  • Set qE = mg to solve for the unknown charge or field strength.
  • The sign of the required charge tells you which plate must be positive: the electric force must point upward to balance gravity, so the charge's sign and the field's direction together must produce an upward force.
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E = V/d gives the field BETWEEN the plates only, and assumes it is uniform

The formula E = V/d treats the field as perfectly uniform between the plates, which is a good approximation away from the edges but breaks down near them. It also only applies WITHIN the gap — do not apply it to find the field outside the plates or beyond their edges. When a question changes the plate separation d without changing V, recompute E from scratch rather than assuming it stays the same: E is inversely proportional to d. ℹ

Drawing the field lines

Field lines between parallel plates are drawn as evenly-spaced STRAIGHT lines running from the positive plate to the negative plate, perpendicular to both plates. Near the edges of the plates the lines curve outward ("fringing") — a diagram-marking question usually wants the straight, evenly-spaced pattern in the main body of the gap, with the edge effect only if specifically asked about.

Practise just this