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
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Let resistivity at a distance '$x$' from left end be $\rho = ({\rho _0} + ax).$ Then electric field intensity at a distance '$x$' from left end will be equal to $E = \frac{{i\rho }}{A} = \frac{{i({\rho _0} + ax)}}{A}$ where $i$ is the current flowing through the conductor. It means $E \propto \rho $ or $E$ varies linearly with distance '$x$'. But at $x = 0$, $E$ has non-zero value. Hence $(b) $ is correct.
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