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A point mass m and charge Q is connectedwitha spring of negligible mass. Initially spring is in its naturallength L. Now a horizontaluniform field E is switched on as shown. Find (a) the maximumseperation between the mass and the wall (b) Find the seperation of the point mass andwall at theequilibriumposition of mass (c ) Find the energy storedinthe spring at theequi librium position of the point mass. |
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Answer» Solution :At maximum seperation,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` seperation `=L+(2qE)/(K)` (b) At EQUILIBRIUM position, `Eq=KX rArr x =(qE)/(K)` `rArr ` seperation `=L+(qE)/(K)` (c ) `U=(1)/(2) Kx^(2) =(1)/(2) K((qE)/(K))^(2) =(q^(2)E^(2))/(2K)` |
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