Electric force between point charges

Physics A2 · Electric fields. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Coulomb's law gives the force between two point charges: it is proportional to the product of the charges and inversely proportional to the square of the distance between them. Like charges repel and unlike charges attract. The force acts along the line joining the charges, and each charge feels a force of the same size.

Because it is an inverse-square law, doubling the separation makes the force four times smaller, and halving it makes the force four times larger.

A charged conducting sphere is not a point, but for any point outside it the charge behaves as if it were all at the centre of the sphere. So always measure r from the centre, not from the surface.

Rules to remember

Common mistake

Students forget to square the distance, or leave the charges in μC. Change every charge to coulombs and every distance to metres, then square r.

Worked example

Point charges of +2.0 μC and +6.0 μC are 0.30 m apart in a vacuum. What is the force between them?

  1. Q1Q2 = 2.0 × 10−6 × 6.0 × 10−6 = 1.2 × 10−11 C2, and r2 = 0.302 = 0.090 m2.
  2. F = 8.99 × 109 × 1.2 × 10−11 ÷ 0.090 = 0.108 ÷ 0.090 = 1.2 N.
  3. Both charges are positive, so the force is a repulsion.

Answer: 1.2 N, repulsive.

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