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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. Usem as mass , L as length of each thread. The angle made by each thread with the vertical is theta. Calculate the charge on objects. |
Answer» Solution :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 ))` |
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