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In the given figure ABC is a non-conducting semi-circular wire of radius ‘a’ carrying a total charge Q uniformly distributed on it and a point charge q is at its centre. Ends of the wire are attached to two separate springs each having spring constant k as shown in the figure. In the given position system is in equilibrium. Now the point charge is suddenly removed. The amplitude of the resulting oscillation is xqQ8π2ε0a2k. Ignoring any force other than spring force and electrostatic force find the value of ‘x’?

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answer is 2.

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Detailed Solution

F=∫dFcos⁡θ=∫14πε0qλR(dθ)R2cos⁡θ=14πε0qλR(sin⁡θ)−π/2π/2=2qλ4πε0R⇒2kA=2qλ4πε0R⇒kA=q4πε0RQπR⇒A=Qq4π2ε0a2k∵R=a⇒A=2Qq8π2ε0a2k⇒x=2

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In the given figure ABC is a non-conducting semi-circular wire of radius ‘a’ carrying a total charge Q uniformly distributed on it and a point charge q is at its centre. Ends of the wire are attached to two separate springs each having spring constant k as shown in the figure. In the given position system is in equilibrium. Now the point charge is suddenly removed. The amplitude of the resulting oscillation is xqQ8π2ε0a2k. Ignoring any force other than spring force and electrostatic force find the value of ‘x’?