A thin wire of length L and cross-sectional area A oriented in the x-direction is made up of an ohmic material whose resistivity varies along the wire according to the empirical law `rho = rho_(0)e^(- x //lL)`
(i) Determine how the field with in wire varies with position if the end at x=0 is at potential `V_(0)` greater than the end at x=L.
(ii) How does potential varies as you move along the wire ?
(Iii) What is resistance of the wire ?

Answer

(a)`R=rho_(0)L/A((e-1)/e),i=V_(0)/R,`
(b)`V_((X))=(V_(o)(e^(-X//L)))/(1-e^(-1))`