If the distance between two charges is halved, what happens to the electric force?

If the distance between two charges is halved, what happens to the electric force?

• A. The force becomes four times larger.
• B. The force becomes two times larger.
• C. The force becomes half as large.
• D. The force remains the same.

Answer: (A)

The main concept is how electric force between two point charges depends on distance through Coulomb’s law: F is proportional to 1 over the distance squared, F ∝ 1/r^2. If the separation is halved, replace r with r/2 in the formula: F' = k q1 q2 / (r/2)^2 = k q1 q2 / (r^2/4) = 4 k q1 q2 / r^2 = 4F. So the force becomes four times larger. The direction (attractive or repulsive) stays the same, determined by the signs of the charges, while the magnitude increases by a factor of four due to the inverse-square relationship.

The main concept is how electric force between two point charges depends on distance through Coulomb’s law: F is proportional to 1 over the distance squared, F ∝ 1/r^2. If the separation is halved, replace r with r/2 in the formula: F' = k q1 q2 / (r/2)^2 = k q1 q2 / (r^2/4) = 4 k q1 q2 / r^2 = 4F. So the force becomes four times larger. The direction (attractive or repulsive) stays the same, determined by the signs of the charges, while the magnitude increases by a factor of four due to the inverse-square relationship.