Question

A charge q is placed at the centre of the line joining 2 equal charges +Q.the system of three charges will be in equilibrium if q is equal to ____options are q/2,-q/4,q/4,-q/2...which option is correct?

Answer 1

A charge q is placed at the center of the line joining two equal charges Q

https://s3mn.mnimgs.com/img/shared/discuss_editlive/2191102/2013_01_25_22_13_05/image3759919087923979063.jpg

Here,

OA = AB = x/2

OB = x

Force on the charge at B due to the charge at O is,

F1 = kQ2/x2

Force on the charge at B due to the charge at A is,

F2 = kQq/(x/2)2

Now, for the system to be in equilibrium the force on one of the Q due to the other Q must be equal to the force on that Q by q.

Therefore,
F1=F2kQ2x2=kQq(x2/)2 q = Q4

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