Question

A point mass `m` and charge `q` is connected with a spring of negligible mass with natural length `L`., Initially spring is in natural length .Now a horizontal unifrom electric field `E` is switched on as shown .Find (a) The maximum separation between the mass and the well
(b) Find the separation of the point mass and wall at the equilbrium position of mass
(c ) Find the energy stored in the spring at the equilirbium position of the point mass
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Answer 1

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)(x_(0)` maximum elongation)
`rArr x_(0)=(2qE)/(K),:.`separation =`L+(2qE)/(k)`
(b) At equilateral position `EqEq=kxrArr 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)`