Two metal spheres, one fo radius R and the other of radius 2R, both have same surface charge density s. They are brought in contact and seprated. What will be new surface charge densitites on them ?

Explanation

The charges on two metal spheres, before coming in contact, are given by
`Q=sigma.4piR^(2)`
`Q_(2)=sigma.4pi(2R^(2))`
`=4(sigma.4piR^(2))=4Q_(1)`
Let the charges on two metal spheres, after coming in contact becomes `Q_(1)' and Q_(2)'`
Now applying law of conservation of charges is given by ltBrgt `Q_(1)'+Q_(2)'=Q_(1)+Q_(2)=5Q_(1)`
`=5(sigma.4piR^(2))`
After coming in contact, they acquire equal potentials. therefore, we have
`(1)/(4piepsi_(0))(Q_(1)')/(R)=(1)/(4piepsi_(0))(Q_(2)')/(R)`
On solving, we get
`thereforeQ_(1)'=(5)/(3)(sigma.4piR^(2)) and Q_(2)'=(10)/(3)(sigma.4piR^(2))`
`thereforesigma_(1)=5//3sigma and thereforesigma_(2)=(5)/(6)sigma`