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Equal charges q are fixed at x = -a and x = +a on the x-axis. A particle of mass m and charge q0 = q/2 placed at the origin is displaced a small distance y (with y << a) along the y-axis. The net force on it is proportional to:

1. y
2. -y
3. 1/y
4. -1/y

Correct answer: -y

Solution

Each fixed charge repels q0. By symmetry, horizontal components cancel and the resultant is along -y (restoring, toward the origin). For y << a, the resultant magnitude is proportional to y, so the force is proportional to -y (a restoring, SHM-type force).

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