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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 : (ε₀ is the permittivity of vacuum, neglect gravitational forces)

Asked in Re-NEET 2026 · Energy conservation and closest approach

• (1) √(3Qq)/(4πε₀mR)
• (2) √(2Qq)/(3πε₀mR)
• (3) √(Qq)/(3πε₀mR)
• (4) √(Qq)/(4πε₀mR)

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives this: v²=(3kQq)/(mR) is more than even a fall from infinity could give, (2kQq)/(mR).
• (2) No single slip gives this: v²=(8kQq)/(3mR) is more than even a fall from infinity could give, (2kQq)/(mR).
• (4) No single slip gives this: v²=(kQq)/(mR) means a kinetic energy of only (kQq)/(2R), less than the (2kQq)/(3R) the field supplies.

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