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A charge q is placed at centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium , if q is equal to

A charge q is placed at centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium , if q is equal to

Grade:12

2 Answers

Arun
25750 Points
5 years ago

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

For the system to be in equilibrium,

F1 + F2 = 0

=> kQ2/x2 + kQq/(x/2)2 = 0

=> q = -Q/4

Khimraj
3007 Points
5 years ago
Let the distance between charges Q is r.
Then charge q is olaced at distance r/2 from each
Then for equilibrium
(KQq)/(r/2)2 + KQQ/r2 = 0
Then q = -Q/4.
Hope it clears.

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