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A charged sphere is connected to a similar uncharged sphere . Then the percentage loss of enery is

Asked by Deepak 4th August 2018, 3:55 PM
Answered by Expert
Answer:
Let R be the radius of the sphere and q Coulomb be the charge on the sphere.
Initial Stored energy on the sphere =  begin mathsize 12px style 1 half q squared over C space................... left parenthesis 1 right parenthesis
end style
where C is the capacitance of the sphere which is equal to 4πεoR.
 
Once the charged sphere is made contact with similar sphere,
both spheres share the charge uniformly and each sphere will have charge q/2 Coulomb
Since the capacitance is related to radius and radius of each sphere is same, capacitance remains constant.
 
Now the energy stored in both the capacitors = begin mathsize 12px style 1 half fraction numerator q squared over denominator 4 C end fraction space plus space fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction fraction numerator begin display style q squared end style over denominator begin display style 4 C end style end fraction space equals space fraction numerator begin display style 1 end style over denominator begin display style 4 end style end fraction fraction numerator begin display style q squared end style over denominator begin display style C end style end fraction space........... left parenthesis 2 right parenthesis end style
By comparing eqn(1) and (2), we get loss of energy is 50%
Answered by Expert 4th August 2018, 4:37 PM
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