Two identical point charges +q are fixed at a distance 2a apart. A third charge -q is placed at the midpoint between them. If the middle charge is slightly displaced by a small distance x along the line joining the charges and released, what type of motion will it undergo?

Answer and explanation

Correct answer: B. It will accelerate toward the nearer charge without oscillating

- The distance to the right charge becomes , so the attractive force to the right is .
- The distance to the left charge becomes , so the attractive force to the left is .
  1. Step 1: Let the charges be at and , with the middle charge initially at in equilibrium.
  2. Step 2: When is displaced by a small distance toward the charge at :
  3. Step 3: Since , .
  4. Step 4: The net electrostatic force acts to the right, in the direction of displacement, pulling further away from the center toward the right charge.
  5. Step 5: Because the net force is not a restoring force, the equilibrium is unstable along the axis, and the charge will accelerate toward the nearer positive charge without oscillating.
Answer
It will accelerate toward the nearer positive charge without oscillating (unstable equilibrium)
Why not the others: 'It will execute Simple Harmonic Motion' would occur if the middle charge were positive (where the force is restoring), or if the negative charge were displaced perpendicular to the axis; 'Neutral equilibrium' requires net force to remain zero everywhere; 'Orbit in a circle' requires perpendicular initial velocity.

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