A body of mass M and charge q is connected to a spring of spring constant k. It is oscillating along x-direction about its equilibrium position, taken to be at x = 0 with an amplitude A. An electric field E is applied along the x-direction. Which of the following statement is correct ?

Options

A. The total energy of the system is `1/2 momega^2 A^2 +1/2 (q^2E^2)/k`
B. The new equilibrium position is at a distance `(2qE)/k` from x=0
C. The new equilibrium position is at a distance `(qE)/(2k)` from x=0
D. The total energy of the system is `1/2 momega^2 A^2 -1/2 (q^2E^2)/k`

Answer

A

Explanation

New equilibriula position will be shifted to point where resultant force on body becomes zero. Let `x_0` be the elongation of spring for new equilibrium then
we can write
`kx_0=qE rArr x_0=(qE)/k`
Energy =`1/2momega^2 A^2 +1/2k("qE"/k)^2 =1/2 momega^2 A^2 +1/2 (q^2 E^2)/k`