Coulomb's law and electric field

MDCAT Physics · Physics · Electrostatics. 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 says that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation. Like charges repel and unlike charges attract. The two charges feel equal and opposite forces. An insulating medium between the charges makes the force smaller by a factor equal to its relative permittivity.

An electric field is a region where a charge feels a force. Field strength is the force per unit positive charge, so its direction is the way a positive charge would be pushed. A negative charge is pushed the opposite way. With several charges, add the forces or fields as vectors.

Rules to remember

Common mistake

Forgetting to square the distance, or leaving charges in μC or nC and distances in cm. Convert to C and m before you substitute.

Worked example

Charges of +3.0 μC and −4.0 μC are 0.30 m apart. Taking k = 9 × 109 N m2 C−2, find the force between them in a vacuum, and in an oil of relative permittivity 2.0.

  1. q1q2 = 3.0 × 10−6 × 4.0 × 10−6 = 1.2 × 10−11 C2, and r2 = 0.302 = 0.090 m2.
  2. F = 9 × 109 × 1.2 × 10−11 ÷ 0.090 = 0.108 ÷ 0.090 = 1.2 N.
  3. In the oil: F = 1.2 ÷ 2.0 = 0.60 N.

Answer: 1.2 N in a vacuum and 0.60 N in the oil, attractive in both cases

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