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Three point charges, +Q, q, and +Q, are located on the x-axis at x = d/2 and x = d from the origin as specified. If the resultant force on a +Q charge placed at x = 0 is zero, what must be the value of q?

1. −Q/4
2. +Q/2
3. +Q/4
4. −Q/2

Correct answer: −Q/4

Solution

On the +Q at x=0: the +Q at x=d repels it, while q at x=d/2 must pull it back. Balancing kQ^2/d^2 = k Q|q|/(d/2)^2 = 4kQ|q|/d^2 gives |q| = Q/4, and q must be negative, so q = -Q/4.

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