Question

There are two fixed spheres of charges Q and 4Q and the distance between their centres is 6R. The Radius of first sphere is R and radius of the secind one is 2R. A charge -q is to be projected from the along the line joining their centres ( it is on the surface of the sphere with radius R), so that  it can reach the surface of other solid sphere of charge 4Q. What will be the minimum velocity to be given so that it reaches there?

sir i have used energy conservation in this problem :

-kqQ/R - kQ4q/5R +.5 mv^2 = -kQq/4r - kqQ4/2R 

but im not getting the answer .....is anything left in ths  ..please telll

Joshi sir comment

first find a point midway between the two spheres where net E will be 0

Then consider v = 0 at that point and compare the potential energy + kinetic energy of the starting point and that obtained point.

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