A fixed uniformly charged insulating sphere of radius R carries total charge +Q. A particle of charge -q (q ≪ Q) and mass m is released from rest at distance 3R from the centre. Neglect gravity. Find its speed when it reaches the sphere's surface.
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Question

A fixed uniformly charged insulating sphere of radius R carries total charge +Q. A particle of charge -q (q ≪ Q) and mass m is released from rest at distance 3R from the centre. Neglect gravity. Find its speed when it reaches the sphere's surface.

Options

G1 Physics · Accepted Answer

Step 1: At all external points, the uniformly charged sphere produces potential V(r) = Q/(4πε₀r). Step 2: Potential energy of the negative charge is U(r) = −Qq/(4πε₀r). Step 3: Initial kinetic energy is zero at r = 3R. Conservation of energy gives (1/2)mv² = U(3R) − U(R). Step 4: (1/2)mv² = [−Qq/(12πε₀R)] − [−Qq/(4πε₀R)] = Qq/(6πε₀R). Step 5: v² = Qq/(3πε₀mR). Final answer: v = √[Qq/(3πε₀mR)] (Option C).

A fixed uniformly charged insulating sphere of radius R carries total charge +Q. A particle of charge −q (q ≪ Q) and mass m is released from rest at distance 3R from the centre. Neglect gravity. Find its speed when it reaches the sphere's surface.