Electric fields

An electric field is the region around a charge where other charges feel a force. Field strength E is the force on each coulomb of charge placed there. Fields can be drawn with lines: radial around a point charge, and uniform (parallel and evenly spaced) between two charged plates – the arrangement used in inkjet printers, cathode-ray tubes and particle accelerators.

Key facts

  • E = F ÷ q (N/C), so F = qE.
  • Point charge: E = kQ ÷ r², with k = 9.0 × 10⁹ N m²/C².
  • Between parallel plates: E = V ÷ d (V/m, the same as N/C).
  • Field lines point from + to −, never cross, and are closer where the field is stronger.
  • Work done on a charge moved through a p.d.: W = qV; an electron accelerated through V gains eV of kinetic energy.
  • Fields from several charges add as vectors.

Worked examples

Example 1

Find the field strength 20 cm from a +8 nC point charge.

  1. Substitute E = 9.0 × 10⁹ × 8 × 10⁻⁹ ÷ 0.20²
  2. Work it out E = 72 ÷ 0.04 = 1800 N/C
  3. The charge is positive, so the field points away from it.

Answer: 1800 N/C, pointing away from the charge

Example 2

Plates 4 mm apart have 200 V between them. Find the field strength and the force on a 3 nC droplet between them.

  1. E = V ÷ d E = 200 ÷ 0.004 = 50 000 V/m
  2. F = qE F = 3 × 10⁻⁹ × 50 000 = 1.5 × 10⁻⁴ N

Answer: 50 000 V/m; 1.5 × 10⁻⁴ N

Example 3

Charges of +4 nC and −4 nC are 20 cm apart. Find the field at the midpoint.

  1. Each is 10 cm away E = 9.0 × 10⁹ × 4 × 10⁻⁹ ÷ 0.10² = 3600 N/C
  2. From +: away from +, i.e. towards −. From −: towards −. Same direction.
  3. Total 3600 + 3600 = 7200 N/C towards the negative charge

Answer: 7200 N/C towards the negative charge