A cylindrical conductor has uniform cross-section. Resistivity of its material increase linearly from left end to right end. If a constant current is flowing through it and at a section distance x from left end, magnitude of electric field intensity is E , which of the following graphs is correct

Options

A.
B.
C.
D.

Answer

B

Explanation

Resistivity `rho = rho_(0) + kx, k` and `rho_(0)` are constant.
Since, `E = V/I = (iR)/I = (i rho)/A rArr E = (i(rho_(0) + kx))/A`
`E prop rho`, also `E prop x` but when x = 0, `E ne 0`