A copper wire of length $10 ext{ m}$ and radius $\frac{10^{-2}}{\sqrt{\pi}} ext{ m}$ has electrical resistan

Question

A copper wire of length $10	ext{ m}$ and radius $\frac{10^{-2}}{\sqrt{\pi}}	ext{ m}$ has electrical resistance of $10\ \Omega$. The current density in the wire for an electric field strength of $10	ext{ V/m}$ is

Accepted Answer

Resistance $R = ho \frac{L}{A}$. Current density $j = \sigma E = \frac{1}{ho} E$. Since $R = \frac{ho L}{A}$, we have $\frac{1}{ho} = \frac{L}{RA}$. Thus, $j = \frac{E L}{RA}$. Substituting the values: $j = \frac{10 	imes 10}{10 	imes \pi (\frac{10^{-2}}{\sqrt{\pi}})^2} = \frac{100}{10 	imes \pi 	imes \frac{10^{-4}}{\pi}} = \frac{100}{10^{-3}} = 10^5	ext{ A/m}^2$.

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