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).
D. Qq 3 _0 mR
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
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