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Please answer the following question with explanation
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Asked by deepakudgiri29 | 02 May, 2019, 11:07: PM
answered-by-expert Expert Answer
Figure shows the forces Fg and Fe acting on charged spheres in hemisphere of radius R at equilibrium position.
Fg = mg is the gravitational force, where m is mass of sphere. Fe = begin mathsize 12px style space fraction numerator begin display style Q squared end style over denominator begin display style 4 πε subscript straight o straight d squared end style end fraction end style , where d is the separation distance between spheres.
Let us resolve the two forces so that one component is normal to the contact point and other one parallel to tangent at contact point.
 
As shown in figure, balancing components of two forces are Fg cosθ and Fe sinθ.
 
Hence  Fg cosθ = Fesinθ    or  begin mathsize 12px style space fraction numerator begin display style Q squared end style over denominator begin display style 4 πε subscript straight o straight d squared end style end fraction space sin theta space equals space m g space cos theta end style
Hence begin mathsize 12px style Q space equals space square root of fraction numerator 2 space m space g space straight pi space straight epsilon subscript straight o straight d cubed over denominator square root of R squared minus begin display style d squared over 4 end style end root end fraction end root end style
Answered by Thiyagarajan K | 03 May, 2019, 10:29: AM

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