Two identical small charged spheres, each having a mass m, hang in equilibrium as shown in fig. the length of each string is l, and the angle made by any string with the vertical is `theta`. Find the magnitude of the charge on each sphere.

Explanation

The force acting on the sphere are tension in the string `T` force of gravity `'mg'` and repulsice force `F_(e)`
`T costheta=mg…..(1)`
`T sintheta=F_(e)=(Kq_(2))/(r^(2))….(2)`
from (1) and (2)
`F_(e)=mg "tan" theta ,(Kq_(2))/(r^(2))=mg tan theta`
form fig.`r=2l sin theta,(1)/(4 theta epsilon_(0))(q^(2))/(2lsintheta)^(2)=mg tan theta`
`q=sqrt(16 piepsilon_(0)l^(2)mg tanthetasin^(2)theta)`