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.

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)mv²

Initial E.P.E = kQq / r

Final E.P.E = kQq(3R² - R₁²) / (2R³)

where k = 9 × 10⁹ , R₁ = R/2, R = radius of the non conducting sphere.

                                  r = initial seperation of the point mass from the centre of the sphere.