Electric field of a point charge

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

A point charge Q produces a radial field: the field lines are straight lines spreading out from the charge. The field points away from a positive charge and towards a negative charge.

The field strength follows an inverse-square law. At twice the distance the field is one quarter as strong, and at three times the distance it is one ninth. The same formula works outside a charged conducting sphere if r is measured from its centre.

Field strength is a vector. When there are two charges, work out the field of each at the point, decide each direction by imagining a small positive charge placed there, then add them if they point the same way and subtract if they are opposite.

Rules to remember

Common mistake

Students add the sizes of two fields without thinking about direction. Between two like charges the fields are in opposite directions and must be subtracted; between unlike charges they add.

Worked example

Point charges of +2.0 nC and +8.0 nC are 0.30 m apart in a vacuum. What is the electric field strength at the midpoint between them?

  1. The midpoint is 0.15 m from each charge, so r2 = 0.0225 m2.
  2. Field of the +2.0 nC charge: 8.99 × 109 × 2.0 × 10−9 ÷ 0.0225 = 799 N C−1, pointing away from it.
  3. Field of the +8.0 nC charge: 8.99 × 109 × 8.0 × 10−9 ÷ 0.0225 = 3196 N C−1, pointing away from it.
  4. The two fields are opposite, so the resultant = 3196 − 799 = 2397 N C−1, in the direction of the larger field.

Answer: 2.4 × 103 N C−1, directed towards the +2.0 nC charge.

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