Question

A conductor is carrying a 2 mA current. How many free-electron have crossed through a given cross-section of the conductor in 20 seconds?

Answer 1

Step1:- Given data

current through a conductor is $i=2mA=2\times {10}^{-3}A$ ($1meter=1000mm$)

time taken is t =20 seconds.

(Note:- Charge on an electron $e=1.6\times {10}^{-19}coulomb$.)

Step2:- Finding the total charge flown in 20 sec

$$\begin{gathered} charge\left(q\right)=i\times t \\ =2\times {10}^{-3}\times 20 \\ =4\times {10}^{-2}coulomb \end{gathered}$$

Step3:- Finding number ($n$) electron flow through the conductor in 20 seconds.

$$\begin{gathered} q=ne=4\times {10}^{-2}coulomb \\ n=\frac{4\times {10}^{-2}}{1.6\times {10}^{-19}} \\ =\frac{1}{4}\times {10}^{18}=0.25\times {10}^{18} \\ =2.5\times {10}^{17}C. \end{gathered}$$

Hence $2.5\times {10}^{17}$ free-electron has crossed through a given cross-sectional area in 20 seconds.