Which of the following is true?
(A) The equilibrium of a charged particle under the action of coulomb force alone can never be stable.
(B) A hollow metal sphere placed on an insulating stand is charged positively. The electric potential inside is same as on surface
(C) A free electron and a free proton are placed in a uniform field, both will experience same magnitude of the force
(D) A free electron and a free proton are placed in a uniform field, both will experience same acceleration
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B) and (C) Only
(A) The equilibrium of a charged particle under the action of coulomb force alone can never be stable. — Correct. This is Earnshaw’s theorem: a charge placed among other fixed charges cannot sit at a point of stable equilibrium, because the potential has no minimum in all directions there.
(B) A hollow metal sphere placed on an insulating stand is charged positively. The electric potential inside is same as on surface — Correct. The charge sits on the outer surface and the field inside is zero, so the potential is constant throughout the inside and equals the surface value.
(C) A free electron and a free proton are placed in a uniform field, both will experience same magnitude of the force — Correct. \( F = qE \) and both charges have the magnitude \( e \).
(D) A free electron and a free proton are placed in a uniform field, both will experience same acceleration — Incorrect. The acceleration is \( a = F/m \); the forces are equal in magnitude but the electron is about 1836 times lighter, so its acceleration is much larger (and opposite in direction).