Q. A cylindrical conductor has uniform cross-section. Resistivity of its material increases 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
A)
B)
C)
D)
Explanation
(b) Let resistivity at a distance $'x^{'}$ from left end be $\rho = \left( \rho_{0} + ax \right).$ Then electric field intensity at a distance $'x^{'}$ from left and will be equal to $E = \frac{i\rho}{A} = \frac{i\left( \rho_{0} + ax \right)}{A}$
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
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.