Consider a fixed uniformly charged insulating sphere with radius R and total charge +Q . A point charge -q ( q Q ) with mass m is released from rest at a distance of 3R from the centre of the charged sphere. When the point charge reaches the surface of the sphere, its speed is : ( ₀ is the permittivity of vacuum, neglect gravitational forces).

Step-by-step solution

Initial potential energy of the system when the charge -q is at a distance of 3R from the centre is: U_i = - 1 4 ₀ Qq 3R Final potential energy of the system when the charge reaches the surface of the sphere (distance R from the centre) is: U_f = - 1 4 ₀ Qq R According to the principle of conservation of mechanical energy: K_i + U_i = K_f + U_f 0 - Qq 12 ₀ R = 1 2 mv^2 - Qq 4 ₀ R 1 2 mv^2 = Qq 4 ₀ R - Qq 12 ₀ R 1 2 mv^2 = Qq 4 ₀ R ( 1 - 1 3 ) 1 2 mv^2 = 2Qq 12 ₀ R v^2 = Qq 3 ₀ mR v = Qq 3 ₀ mR Answer: Qq 3 ₀ mR