A fixed uniformly charged solid non-conducting sphere of radius R has a total positive charge Q . A small particle of mass m and negative charge -q is released from rest at a distance 4R from the centre of the sphere. The particle moves towards the sphere under the influence of the electrostatic force. What is the kinetic energy of the particle just before it strikes the surface of the sphere?

Step-by-step solution

The electrostatic field is conservative, so the mechanical energy of the particle is conserved during its motion. Let the initial position be at a distance r_i = 4R and the final position be at the surface of the sphere, r_f = R . The electric potential at a distance r ( r R ) from the centre of the sphere is V(r) = 1 4 ₀ Q r . The initial potential energy of the system is: U_i = -q V(4R) = -q ( 1 4 ₀ Q 4R ) = - qQ 16 ₀ R The final potential energy of the system just before striking the surface is: U_f = -q V(R) =