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If the distance between two point charges is doubled, how does the force between

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Question: If the distance between two point charges is doubled, how does the force between them change according to Coulomb\'s law?

Options:

  1. It doubles
  2. It quadruples
  3. It halves
  4. It becomes one-fourth

Correct Answer: It becomes one-fourth

Solution: 

According to Coulomb\'s law, the force F between two point charges is inversely proportional to the square of the distance r between them. If the distance is doubled, the force becomes F/4.

If the distance between two point charges is doubled, how does the force between

Practice Questions

Q1
If the distance between two point charges is doubled, how does the force between them change according to Coulomb's law?
  1. It doubles
  2. It quadruples
  3. It halves
  4. It becomes one-fourth

Questions & Step-by-Step Solutions

If the distance between two point charges is doubled, how does the force between them change according to Coulomb's law?
  • Step 1: Understand Coulomb's law, which states that the force F between two point charges is given by the formula F = k * (q1 * q2) / r^2, where k is a constant, q1 and q2 are the charges, and r is the distance between them.
  • Step 2: Note that the force F is inversely proportional to the square of the distance r. This means that if the distance increases, the force decreases.
  • Step 3: If the distance r is doubled, we replace r with 2r in the formula. So, the new force F' becomes F' = k * (q1 * q2) / (2r)^2.
  • Step 4: Calculate (2r)^2, which is 4r^2. So, the new force F' can be rewritten as F' = k * (q1 * q2) / 4r^2.
  • Step 5: Compare the new force F' with the original force F. We see that F' = F / 4, meaning the new force is one-fourth of the original force.
  • Coulomb's Law – Coulomb's law states that the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
  • Inverse Square Law – The relationship that describes how a physical quantity decreases with the square of the distance from the source.
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