Electrostatic Potential and Capacitance · Question 42

A particle of mass 'm' and charge 'q' is fastened to one end 'A' of a massless string having equilibrium length l, whose other end is fixed at point 'O'. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x-axis is [figure]

1. qEl2m
2. qEl4m
3. qElm
4. 2qElm

Answer

(3) qElm

Solution

The string stays taut; the particle moves on a circle of radius l about O from 60 to 0 (the x-axis).

Displacement along the field (x-direction): x = l - l 60 = l2

Work done by the electric force: W = qE x = qEl2 (tension does no work)

Work-energy theorem: 12mv2 = qEl2

v = qElm

Answer: (3)