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Circuit and electromagnetism basics

How does the magnitude of the electrostatic (Coulomb) force between two point charges in vacuum change if the distance is doubled without changing the charges?

  1. AIt becomes 1/2
  2. BIt doubles
  3. CIt becomes 1/4
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Answer: C. It becomes 1/4

By Coulomb's law the force is F = k × q1 × q2/r², inversely proportional to the square of the distance r. Doubling the distance makes the force 1/2² = 1/4 as large. In vacuum k ≈ 9×10⁹ N·m²/C², and filling the surroundings with a material of relative permittivity εr reduces the force to 1/εr. Like charges repel and unlike charges attract.

  • A. 1/2 assumes the force is inversely proportional to distance, forgetting the square.
  • B. Doubling would mean the force is proportional to distance, which is wrong.
  • C. Correct. The force is inversely proportional to the square of the distance, so it becomes 1/4.
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