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Three charges +q, +2q and +4q are joined in a line by two strings, AB and BC, as shown. Find the ratio of the tensions in strings AB and BC.

1. 1: 2
2. 1: 3
3. 2: 1
4. 3: 1

Correct answer: 2: 1

Solution

For charges in a line connected by strings, the tension in each string equals the net electrostatic force that must be balanced across that string. Considering the standard configuration (+q, +2q, +4q at equal successive separations with strings AB between +q and +2q, BC between +2q and +4q), the tension AB supports charge +q against the repulsion of +2q and +4q, while BC supports charge +4q. Working out the net forces gives T_AB: T_BC = 2: 1.

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