QuestionJune 12, 2025

Two charges with magnitude Q experience a force F when held a distance r apart. What is the force between two charges of magnitude 2Q held a distance 2r apart? F/2 4F F/4 F 16F

Two charges with magnitude Q experience a force F when held a distance r apart. What is the force between two charges of magnitude 2Q held a distance 2r apart? F/2 4F F/4 F 16F
Two charges with magnitude Q experience a force F when held a distance r apart. What is the force between two charges of magnitude 2Q held a distance 2r apart? F/2 4F F/4 F 16F

Solution
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Answer

F Explanation 1. Apply Coulomb's Law The force between two charges is given by **F = k \frac{Q_1 Q_2}{r^2}**. For initial charges, F = k \frac{Q \cdot Q}{r^2} = k \frac{Q^2}{r^2}. 2. Calculate New Force For new charges, the force is F' = k \frac{(2Q) \cdot (2Q)}{(2r)^2} = k \frac{4Q^2}{4r^2} = k \frac{Q^2}{r^2}. 3. Compare Forces Since F' = F, the force remains unchanged.

Explanation

1. Apply Coulomb's Law<br /> The force between two charges is given by **$F = k \frac{Q_1 Q_2}{r^2}$**. For initial charges, $F = k \frac{Q \cdot Q}{r^2} = k \frac{Q^2}{r^2}$.<br /><br />2. Calculate New Force<br /> For new charges, the force is $F' = k \frac{(2Q) \cdot (2Q)}{(2r)^2} = k \frac{4Q^2}{4r^2} = k \frac{Q^2}{r^2}$.<br /><br />3. Compare Forces<br /> Since $F' = F$, the force remains unchanged.
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