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A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is $\rho$, how long will the charges take to travel a distance $\mathrm{d}$ ?
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Verified Answer
The correct answer is:
$\frac{\rho \mathrm{dA}}{\mathrm{I}}$
$\frac{\rho \mathrm{dA}}{\mathrm{I}}$
Charge density
$$
\begin{aligned}
&\rho=\frac{\text { charge }}{\text { volume }}=\frac{q}{A d} \Rightarrow q=\rho A d \\
&\text { Also, } q=I T \Rightarrow T=\frac{q}{I}=\frac{\rho A d}{I}
\end{aligned}
$$
$$
\begin{aligned}
&\rho=\frac{\text { charge }}{\text { volume }}=\frac{q}{A d} \Rightarrow q=\rho A d \\
&\text { Also, } q=I T \Rightarrow T=\frac{q}{I}=\frac{\rho A d}{I}
\end{aligned}
$$
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