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Coulomb's Law and Force Between Point Charges

Coulomb's law states that the electrostatic force between two stationary point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them, acting along the line joining the charges.

In one line: Product of charges on top, square of distance below; signs tell direction, not the size of magnitude.

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Understand it

  • For two point charges q1 and q2 separated by distance r in vacuum, the magnitude of force is F = (1/4πε0)(|q1q2|/r2).
  • The constant 1/4πε0 is approximately 9 × 109 N m2 C−2.
  • Like charges repel and unlike charges attract.
  • The force on each charge has equal magnitude and opposite direction.
  • Coulomb's law is valid for point charges or spherically symmetric charge distributions when separation is measured between centres.

Example

Two charges +2 microC and +3 microC separated by 0.30 m repel each other with force F = 9 × 109 × (2 × 10−6)(3 × 10−6)/(0.30)2 = 0.6 N.

Formula and rule

F = (1/4πε0)(q1q2/r2) in vector form with direction along the line joining the charges.

F is in newton, q1 and q2 in coulomb, r in metre, and 1/4πε0 = 9 × 109 N m2 C−2.

Use only for stationary point charges in electrostatics or equivalent spherical charge distributions.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Charges q1 = +4 microC and q2 = -2 microC are 20 cm apart.

  1. 1Convert: q1 = 4 × 10−6 C, q2 = 2 × 10−6 C, r = 0.20 m.
  2. 2F = 9 × 109 × (4 × 10−6)(2 × 10−6)/(0.20)2 = 1.8 N.
  3. 3Since charges are unlike, the force is attractive.

Method you can reuse

  1. 1Convert all quantities to SI units.
  2. 2Write Coulomb's formula.
  3. 3Substitute magnitudes of charges and distance.
  4. 4Calculate force.
  5. 5Use charge signs to state attraction or repulsion and draw direction if required.

Visual tip

Required diagram: two point charges q1 and q2 separated by distance r, line joining them, force on q1 and force on q2 shown in opposite directions. For unlike charges arrows point toward each other; for like charges arrows point away from each other.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

If the distance between two point charges is doubled, what happens to the electrostatic force?

Think first, then show answer
The force becomes one-fourth of its original value because Coulomb's force varies inversely as r2. When r becomes 2r, the denominator becomes 4r2.

Common wrong answer

For q1 = +4 microC and q2 = -2 microC, answering -1.8 N as force magnitude is wrong. Magnitude is positive; the negative sign is represented through direction or attraction.

Don't mix this up

A frequent mistake is substituting distance in centimetres instead of metres, or using q1 + q2 instead of q1q2.

Exam tip

For numerical questions, first convert microC to C and cm to m. Use signs to decide attraction or repulsion, but use magnitudes for force magnitude.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Asked as a statement with formula and units, a direct numerical, a comparison when distance changes, or a vector-direction question involving two or more charges.
  1. 1

    Enough for 1 mark

    Coulomb's law states that the electrostatic force between two stationary point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them, acting along the line joining the charges.

  2. 2

    Add for 2 marks

    Example: Two charges +2 microC and +3 microC separated by 0.30 m repel each other with force F = 9 × 109 × (2 × 10−6)(3 × 10−6)/(0.30)2 = 0.6 N.

  3. 3

    Add for 3 marks

    For two point charges q1 and q2 separated by distance r in vacuum, the magnitude of force is F = (1/4πε0)(|q1q2|/r2).

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