Two cylindrical conductors with equal cross-sections and different resistivites `rho_(1)` and `rho_(2)` are point end to end. Find the charge at the boundary of the conduction if a current `I` flows from conductor 1 to conductor 2

Explanation

The electric field in conductor 1 is
`E_(1) = (rho_(1) I)/(pi R^(2))`
and that in 2 is `E_(2) = (rho_(2) I)/(pi R^(2))`
Appling Gauss's theorem to a small cylindical pill-box at the boundary.
`- (rho_(1) I)/(pi R^(2)) dS + (rho_(2) I)/(pi R^(2)) dS = (sigma dS)/(epsilon_(0))`
Thus, `sigma = epsilon_(0) (rho_(2) - rho_(1)) (1)/(pi R^(2))`
and charge at the boundary `= epsilon_(0) (rho_(2) - rho_(1)) I`