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Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency: (m = mass of charged particle)

1. (2q²/(πϵ0md³))^(1/2)
2. (πϵ0md³/(2q²))^(1/2)
3. (q²/(2πϵ0md³))^(1/2)
4. (2πϵ0md³/q²)^(1/2)

Correct answer: (q²/(2πϵ0md³))^(1/2)

Solution

The correct option represents the angular frequency of simple harmonic motion for the proton, derived from the net force acting on it due to the two fixed electrons. The force is proportional to the displacement and inversely proportional to the cube of the distance, leading to the specific form of the frequency given by the equation.

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