InterviewSolution
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InterviewSolution
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Consider two conductinbg spheres of radill `R_(1) and R_(2)` with `R_(1)gt R_(2).` If the two are at the same potential, and the larger sphere has more charge than the smaller sphere, thenA. the charge density of smaller sphere is less then that of larger sphere,B. the charge density of smaller sphere is more than tahat of larger sphere.C. both spheres may have same charge density.D. none of these |
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Answer» Correct Answer - B Here ` V_(1) = V_(2) or ( q_(1))/(4pi epsi_(0)R_(1)) = (q_(2))/(4piepsi_(0)R_(2))` `therefore " "(q_(1))/(q_(2)) = (R_(1))/(R_(2)) " "......(i)` Given `R_(1) gt R_(2)` `therefore " "q_(1) gt q_(2)` `therefore` Larger sphere has more charge than the smaller sphere. Now charge densities. `sigma = (q_(1))/(4piR_(1)^(2)) and sigma_(2) = (q_(2))/(4piR_(2)^(2))` `therefore (sigma_(2))/(sigma_(1)) = (q_(2))/(q_(1)) (R_(1)^(2))/(R_(2)^(2)) or (sigma_(2))/(sigma_(1)) = (R_(2))/(R_(1)) (R_(1)^(2))/(R_(2)^(2)) = (R_(1))/(R_(2)) " "("using (i)")` As `R_(1) gt R_(2) ` therefore `sigma_(2) gt sigma_(1)` Charge density of smaller sphere is more thatn the charge density of large sphere. |
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