Question

A cylindrical wire of radius $0.5\text{mm}$ and conductivity $5\times {10}^7\text{S/m}$ is subjected to an electric field of $10\text{mV/m}$. The expected value of current in the wire will be $x^3\pi \text{mA}$. The value of $x$ is

• A. 5.00
• B. 5
• C. 5.0

Answer 1

Answer: (A), (B), (C)

As we know that,
$$J=\sigma E$$$\Rightarrow J=5\times {10}^7\times 10\times {10}^{-3}$

$\Rightarrow J=50\times {10}^4{\text{A/m}}^2$

Current from wire is,
$$I=J\times \pi R^2$$$\Rightarrow I=50\times {10}^4\times \pi \times (0.5\times {10}^{-3}{)}^2\text{A}$

$\Rightarrow I=125\times {10}^{-3}\times \pi \text{A}$

$\Rightarrow I=(5{)}^3\pi \text{mA}$

$\Rightarrow x=5$