Positive charge Q is uniformly distributed throuhout the volume of a dielectic sphere of radius R. A ponit mass having charge +q and mass m is fired towards the centre of the sphere of velocity v from a point A at a distance r(rR) from the centre of the sphere. Find tyhe minimum velocity v so that it can penetrate R/2 distance of the sphere.

Question

Positive charge Q is uniformly distributed throuhout the volume of a dielectic sphere of radius R. A ponit mass having charge +q and mass m is fired towards the centre of the sphere of velocity v from a point A at a distance r(r>R) from the centre of the sphere. Find tyhe minimum velocity v so that it can penetrate R/2 distance of the sphere.

Nagaraju Kandru · Answer

To solve the above problem, we can use conservation of energy. Total initial energy = Total final energy K.E + Initial Electrostatic P.E = Final Electrostatic P.E K.E = (1/2)mv 2 Initial E.P.E = kQq / r Final E.P.E = kQq(3R 2 - R 1 2 ) / (2R 3 ) where k = 9 &times; 10 9 , R 1 = R/2, R = radius of the non conducting sphere. r = initial seperation of the point mass from the centre of the sphere.

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