Question

Conisder a block of conducting material of resistivity $\rho$ shown in fig., Current I enters at A and leaves at D

For current entering at A, the electric field at a distance 'r' from A is?

• A. $\frac{\rho l}{8\pi r^2}$
• B. $\frac{\rho l}{r^2}$
• C. $\frac{\rho l}{2\pi r^2}$
• D. $\frac{\rho l}{4\pi r^2}$

Answer 1

Answer: (C)

$\frac{\rho l}{2\pi r^2}$

Resistivity $=\rho$

current $=9$

$E=\rho \hat{j}=\rho \times \frac{I}{2\pi r^2}$

$V_C-V_B=-\frac{\rho I}{2\pi }{\int }_a^{(a+b)}\frac{1}{r^2}dr$

$=\frac{\rho I}{2\pi }[\frac{1}{a+b}-\frac{1}{a}]$

$V_B-V_C=\frac{\rho I}{2\pi }[\frac{1}{a}-\frac{1}{a+b}]$