Question

If the distance between two charges is doubled, the Coulomb force becomes:

• A. Twice
• B. Half
• C. One-fourth
• D. Four times

Hint:

In Coulomb's law, force varies inversely with the square of distance. If distance doubles, force becomes \(1/4\); if distance triples, force becomes \(1/9\).

Answer 1

The Correct Option is C

Concept: Coulomb's law states that the electrostatic force between two point charges is \[ F = \frac{k q_1 q_2}{r^2} \] where \(q_1, q_2\) = magnitudes of charges, \(r\) = distance between the charges, \(k\) = Coulomb's constant. The force is inversely proportional to the square of the distance between the charges.

Step 1: Write the original force. \[ F = \frac{k q_1 q_2}{r^2} \]

Step 2: Double the distance between the charges. If the distance becomes \(2r\), then \[ F' = \frac{k q_1 q_2}{(2r)^2} \]

Step 3: Simplify the expression. \[ F' = \frac{k q_1 q_2}{4r^2} \] \[ F' = \frac{F}{4} \] Thus, the force becomes one-fourth of the original force.