A point mass m and charge q is connected with a spring of negligible mass with natural length L. Initially spring is in its natural length. Now a horizontal uniform electric fiedl E is switched on as shown. Find
(a) the maximum separation between the mass and the wall
(b) Find the separation of the point mass and wall at the equilibrium position of mass.
(c ) FInd the enery stored in the spring at the equilibrium position of the point mass

Explanation

At maximum separation, velocity of point mass is zero. From work energy theorem, `W_("spring") + W_("field") = 0`
`qEx_(0) - (1)/(2) kx_(0)^(2) = 0` (`x_(0)` is maximum elongation)
`rArr x_(0) = (2qE)/(K) therefore` separation `= L + (2qE)/(k)`
(b) At equilibrium position, Eq = `kx rArr x = (qE)/(k) rArr` separation `= L + (qE)/(k)`
(c ) `U = (1)/(2) kx^(2) = (1)/(2) k ((qE)/(k))^(2) = (q^(2)E^(2))/(2k)`