Two charged metallic spheres of radii`r_(1)` and `r_(2)` are touched and separated. Calculated the ration of their
(i) Charges
(ii) Potential
(ii) Self energy
(iv) Electric field at the surface
(v) Surface cahrge density

Explanation

After touching potential will be same
so `V_(1) = V_(2)`
`k(Q_(1))/(r_(1))= K (Q_(2))/(r_(2))`, then
(i) `(Q_(1))/(Q_(2)) = (r_(1))/(r_(2))`
(ii) `(V_(1))/(V_(2)) = 1 ` or ` V_(1) : V_(2) = 1 :1`
(iii) `:' U= (1)/(2) cv^(2)` so, `U prop C ` or `U prop rimplies ( U_(1))/(U_(2)) = (r_(1))/(r_(2)) `
(iv) `:. E = (v)/(d) ` so, `E = (1)/(d) ` then `(E_(1))/(E_(2)) = ( r_(2))/(r_(1))`
(v) `:. V = ( ar)/( epsilon_(0))`
`implies ` At same potential,
`sigma r = ` constant
`implies (sigma_(1))/(sigma_(2)) = ( r_(2))/(r_(1))`