PYQ NEET- Current Electricity L-10

Question: A copper wire of length $10 \mathrm{~m}$ and radius $\left(\frac{10^{-2}}{\sqrt{\pi}}\right) \mathrm{m}$ has electrical resistance of $10 \Omega$. The current density in the wire for an electric field strength of $10(\mathrm{~V} / \mathrm{m})$ is: (2022)#

A) $10^4 \mathrm{~A} / \mathrm{m}^2$

B) $10^6 \mathrm{~A} / \mathrm{m}^2$

C) $10^{-5} \mathrm{~A} / \mathrm{m}^2$

D) $10^5 \mathrm{~A} / \mathrm{m}^2$

Answer: $10^5 \mathrm{~A} / \mathrm{m}^2$#

Explanation#

Resistance, $R=\rho \frac{L}{A}=\frac{L}{\sigma A}$

$\Rightarrow \sigma=\frac{L}{R A}$

Also current density $j=\sigma E=\frac{L E}{R A}$

$J=\frac{10 \times 10}{10 \times \pi\left(\frac{10^{-2}}{\sqrt{\pi}}\right)^2}=\frac{100}{10 \times \pi \times\left(\frac{10^{-4}}{\pi}\right)}$

$=10^5 \mathrm{~A} / \mathrm{m}^2$