A fixed uniformly charged insulating sphere has radius R and total charge +Q . A point charge -q ( q Q ) is projected radially outward from the surface of the sphere. The initial kinetic energy given to the point charge is exactly half the magnitude of its electrostatic potential energy at the surface. Neglecting gravitational forces, what is the maximum distance from the centre of the sphere reached by the point cha

Step-by-step solution

The electrostatic potential energy of the system when the charge -q is at the surface of the sphere (distance R from the centre) is: U_ surface = - 1 4 ₀ Qq R The magnitude of this potential energy is |U_ surface | = 1 4 ₀ Qq R . The initial kinetic energy given to the charge is half of this magnitude: K_i = 1 2 ( 1 4 ₀ Qq R ) According to the principle of conservation of mechanical energy, the total energy E remains constant: E = K_i + U_ surface = 1 2 ( 1 4 ₀ Qq R ) - 1 4 ₀ Qq R = - 1 2 ( 1 4 ₀ Qq R ) At the maxi