If two point charges of opposite sign are separated by distance r, and the distance is doubled, what happens to the magnitude of the electric force between them?

If two point charges of opposite sign are separated by distance r, and the distance is doubled, what happens to the magnitude of the electric force between them?

• A. It doubles
• B. It remains the same
• C. It becomes half
• D. It becomes one-fourth

Answer: (D)

Coulomb's law shows the electric force between two point charges follows an inverse-square relationship: F is proportional to 1/r^2. If you double the separation, the new force is F' = k|q1 q2|/(2r)^2 = k|q1 q2|/(4r^2), which is one quarter of the original. The opposite signs mean the force is attractive, but the magnitude scales with 1/r^2, so doubling the distance reduces the magnitude to one-fourth.

Coulomb's law shows the electric force between two point charges follows an inverse-square relationship: F is proportional to 1/r^2. If you double the separation, the new force is F' = k|q1 q2|/(2r)^2 = k|q1 q2|/(4r^2), which is one quarter of the original. The opposite signs mean the force is attractive, but the magnitude scales with 1/r^2, so doubling the distance reduces the magnitude to one-fourth.