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 ?

Explanation

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`