Two identically charged spherical objects are suspended from a common point , using two different threads of equal length. Due to repulsion between charges both strings are maintaining a constant angle with the vertical, and both the objects are in equilibrium. Use m as mass , L as length of each thread. The angle made by each thread with the vertical is `theta`. Calculate the charge on objects.

Explanation

T is the tension in the strings. Weight , mg, is acting vertically downwards. Electric force of repulsion between objects is F. Distance between objects can be written as `2L sin theta` . The electric force can be written as :

`F=1/(4piepsilon_0)q^2/(2L sin theta)^2`
Tension (T) is resolved along horizontal and vertical directions. Objects are in equilibrium along horizontal and vertical directions . So we may write the following equations :
`T cos theta =mg`…(i)
`T sin theta = 1/(4piepsilon_0)q^2/(2L sin theta)^2` ….(ii)
Dividing equation (ii) by (i) ,
`(sin theta)/(cos theta)=1/(4piepsilon_0)q^2/(mg(2L sin theta)^2)`
`rArr q=sqrt((16piepsilon_0mgL^2 sin^3 theta)/(cos theta ))`