Question

If the conduction-electron density in copper wire is $n$, the area of cross-section of wire is A and the average drift speed of electron $V_d$, then the net number of electrons crossing a cross-section of the wire in a unit time interval $t$ will be

• A. $n{V}_{d}At$
• B. $ne{V}_{d}At$
• C. $ne{V}_{d}A$
• D. $n{V}_{d}A$

Answer 1

The correct option is A $n{V}_{d}At$

Let the length of the elementary cylinderical wire be $L$.

Distance covered by the electrons in time $t$, $L=V_{d}t$

Volume of the cylinder $V=AL$

$\therefore$ $V=A{V}_{d}t$

Thus net number of electrons crossing cross-section of the wire $N=nV$

$⟹$ $N=n{V}_{d}At$