Question

A current $I$ flows through a cylindrical rod of uniform cross-sectional area $A$ and resistivity $\rho$. The electric flux through the shaded cross-section of rod as shown in figure is:

• A. $\frac{I}{\rho}$
• B. $\rho I$
• C. $\frac{\rho I}{A}$
• D. $\frac{\rho A}{I}$

Answer 1

Answer: (B)

The current density $J$, electric field $E$ at the cross section are related by $J=\frac{E}{\rho}$
Multiplying both side by $A$, we get
$J A=\frac{E A}{\rho}$ or $I=\frac{\phi}{\rho}$ where $\phi$ is electric flux.
or $\phi=\rho I$