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Two metal spheres, one of radius R and the other of radius 2R, both have same surfac charge density sigma. They are brought in contac and separated. What will be new surface charge densites on them ? |
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Answer» Solution :Let charges on metal spheres before contact are `Q_(1)` and `Q_(2)` hence `Q_(1)= sigmaxx4 piR^(2)` and `Q_(2)= sigmaxx4 pi(2R)^(2)` `= sigmaxx16piR^(2)` `4 Q_(1)` Let the charges on metal sphere, after coming in contact becomes `Q_(1)`. and `Q_(2)`.. According to law of conservation of charges `Q_(1) +Q_(2)= Q_(1)+Q_(2)` `= Q_(1)+4Q_(1)` `= 5 Q_(1)` ` = 5 (sigmaxx 4PI R^(2))` When metal spheres come in contact they acquire EQUAL potentials. `:. V_(1)=V_(2)` `(kQ_(1))/(R)= (kQ_(2))/(R)` Putting value of `Q_(1)` and `Q_(2)` in above equations `Q_(1) = (5)/(3) (sigmaxx4piR^(2))` and `Q_(2)= (10)/(2)(sigmaxx4pi R^(2))` `:. sigma_(1) = (5)/(3) sigma ` and `sigma_(2)= (5)/(6) sigma` |
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