Two isolated metallic solid spheres of radii R and 2R are charged such that both of these have same charge density `sigma`. The spheres are located far away from each other and connected by a thin conducting wire. Find the new charge density on the bigger sphere.

Explanation

Before sharing :
Since capacitance `prop` radius, surface area `prop ("radius")^(2)`
`C_(1)=C, A_(1)=A, C_(2)=2C,A_(2)=4A`
`Q_(1)=sigmaA_(1)=sigmaA, Q_(2)=sigmaA_(2)=4 sigmaA`
After sharing:
Common potential,
`V=(Q_(1)+Q_(2))/(C_(1)+C_(2))=(sigmaA+4sigmaA)/(C+2C)=(5sigmaA)/(3C)`
`Q'_(2)=C_(2)V=2C.(5sigmaA)/(3C)=(10)/(3)sigmaA`
Charge density `sigma'_(2)(Q'_(2))/(A_(2))=(((10)/(3)sigmaA))/(4A)=(5sigma)/(6)`