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A point charge +q of mass m is placed at rest at a distance R/2 from the centre of a solid sphere of radius R carrying total charge Q uniformly distributed throughout its volume. The point charge is released from rest. Find the speed of the point charge when it reaches a distance R from the surface of the sphere. (Assume only electrostatic interaction between the two.)
- sqrt(7kQq/16mR)
- sqrt(7kQq/4mR)
- sqrt(5kQq/16mR)
- sqrt(3kQq/4mR)
Correct answer: sqrt(7kQq/4mR)
Solution
The charge starts at R/2 inside the sphere and ends at 2R from the centre. Applying energy conservation with the potential difference gives v² = 7kQq/(4mR).
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