Question

Electric field ,in a straight solid uniform cylindrical conductor of radius R = 2 cm is along the axis of the cylinder and is given by E = K r where K = 1$\times {10}^8$ Volt/Metre${}^2$ and r is the distance (In metre) from the axis of the cylinder. If current in the cylinder is I = 16$\pi$ micro ampere. If the specific conductivity $\sigma =\frac{z}{5}\times {10}^{-8}{\Omega }^{-1}{m}^{-1}$, the value of Z is

• A. 15
• B. 12
• C. 10
• D. 5

Answer 1

Answer: (A)

15

Consider a small circle r distance away from axis with thickness dr.

$J=\sigma E\Rightarrow di=\sigma KrdA=\sigma Kr2\pi rdr$

$di=2\pi \sigma K{r}^{2}dr\Rightarrow i=2\pi \sigma K{\int }_0^R{r}^{2}dr=2/3\times \pi \sigma K{R}^3$

$16\pi \times {10}^{-6}=2/3\times \pi \sigma \times 8\times {10}^{-6}\times {10}^8$

$3\times {10}^{-8}=\sigma$

Therefore $z=15$.