Two idential pith balls , each of mass m and charge +q. are suspended from a point with threads of length l each. If in equiilbrium state ` theta` be the angle which each thread makes with vertical in equilibrium , find value of charge on each ball.

Explanation

The equilibrium state is shown in following Forces acting on either ball are
(i) Weight mg in vertically downward direction.
(ii) Coulombian force ` F= ( 1)/(4 pi in _0) . (q^(2))/( (AB)^(2)) = (1)/( 4 pi in _0) .( q^(2))/( 4 l ^(2) sin ^(2) theta)` in horizontal direction, and
(iii) Tension in thread T.
In equilibrium state ` T cos theta = mg " "...(i) `
and ` " " T sin theta =F= (q^(2))/( 4 pi in _0. 4 l^(2) sin ^(2) theta ) " "...(ii )`
`rArr " " tan theta =( q^(2))/( 4 pi in _0 . 4l^(2) sin ^(2) theta. mg) `
or ` " " q= 2l sin theta sqrt( 4 pi in_0 mg. tan theta ) `
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