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

When the two spheres are brought in contact , charge transfer takes place till their potentials becme same.
`:. V_(1) = V_(2)`
(i) As` V_(1) = V_(2) implies (Q_(1))/(4piepsilon_(0)r_(1))=(Q_(2))/(4piepsilon_(0)r_(2))implies (Q_(1))/(Q_(2))=(r_(1))/(r_(2))`
(ii) `(V_(1))/(V_(2))=1`
(iii) `(U_(1))/(U_(2))= (Q_(1)^(2)//8 pi epsilon_(0)r_(1))/(Q_(2)^(2) //8 pi epsilon_(0)r_(2))= ( Q_(1)^(2))/(Q_(2)^(2))xx(r_(2))/(r_(1))=(r_(1))/(r_(2))`
(iv)` (E_(1))/( E_(2))= ((Q_(1))/(4pi epsilon_(0)r_(1)^(2)))/((Q_(2))/(4piepsilon_(0)r_(2)^(2)))= (Q_(1))/(Q_(2))xx(r_(2)^(2))/(r_(1)^(2))= (r_(2))/(r_(1))`
(v) (v)` (sigma_(1))/( sigma_(2))= ((Q_(1))/(4pi r_(1)^(2)))/((Q_(2))/(4pir_(2)^(2)))= (Q_(1))/(Q_(2))xx(r_(2)^(2))/(r_(1)^(2))= (r_(2))/(r_(1))`
i.e.,`sigma prop (1)/(2)`