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# A charge q is placed at the centre of the line joining two equal point charges, each equal to +Q. This system of three charges will be in equilibrium if q is equal to:

Arun
25763 Points
2 years ago
AQ============(-q)B============QC
let distance between AC =r
and distance between AB=x
hence distance between BC=r-x
now , systems are equilibrium when ,
force b/w AB=force b/w BC=force b/w AC
force b/w AB=force b/w AC
kQq/x^2=KQ^2/r^2
q/x^2=Q/r^2 -------------(1)
force b/w BC =force b/w AC
kqQ/(r-x)^2=kQ^2/r^2
q/(r-x)^2=Q/r^2 ---------------(2)
equation (1) and (2)
x=r/2
now put x=r/2 in equation (1)
q/(r/2)^2=Q/r^2
Q/4=q
hence ,
q=-Q/4

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