KinexiaLEARN PHYSICS

Coulomb's Law — Force Between Two Charges (Worked Example)

Medium
Problem

Two small identical spheres each carry a charge of +2.0 µC. Their centers are 0.50 m apart in air. What is the magnitude of the electrostatic force between them, and is it attractive or repulsive?

Given

  • q₁ = q₂ = +2.0 µC = 2.0 × 10⁻⁶ C

  • r = 0.50 m

  • k = 8.988 × 10⁹ N·m²/C²

Find

Force magnitude F and its direction sense.

Principle

Coulomb's law: the force between point charges is proportional to the product of charges and inversely proportional to the square of their separation.

Formula

Solution

  1. Write the law: F=(8.988×109)(2.0×10−6)(2.0×10−6)/(0.50)2F = (8.988 \times 10^9)(2.0 \times 10^{-6})(2.0 \times 10^{-6})/(0.50)^2

  2. Numerator: (8.988×109)(4.0×10−12)=3.595×10−2(8.988 \times 10^9)(4.0 \times 10^{-12}) = 3.595 \times 10^{-2}

  3. Denominator: 0.250.25; divide: 3.595×10−2/0.25=0.1438 N3.595 \times 10^{-2}/0.25 = 0.1438\ \mathrm{N}

  4. Like charges repel, so the force pushes the spheres apart.

≈ 0.144 N, repulsive

Unit check

(N·m²/C²)(C²)/(m²) = N. Units collapse to newtons — correct.

What this means physically

0.144 N is tiny — about the weight of 15 grams — yet it comes from an invisible charge you could barely feel. Electrostatic forces are enormously strong per unit charge; everyday objects just carry very little net charge.

Common mistake

Forgetting to convert microcoulombs to coulombs (a factor of 10⁻⁶ each — missing it inflates the answer a trillion-fold) or forgetting to square the distance.