Question

It has been estimated that there are about 10^29 free electrons per cubic meter in

copper. Find the average drift velocity (in units of meters per hour) of electrons in a 1.0

mm diameter copper wire carrying a 3A current. Start your clearly shown work from

the definition of current, that is the amount of charge passing a cross-section per unit

time

Answer 1

By the definition of the current we have:

$$I=\dfrac{\Delta Q}{\Delta t}=nAv_dq.$$

From this formula we can find the drift velocity:

$$v_d=\dfrac{3\ A}{10^{29}\ \dfrac{el}{m^3}\cdot\dfrac{\pi(1.0\cdot10^{-3}\ m)^2}{4}\cdot1.6\cdot10^{-19}\ C}=2.4\cdot10^{-4}\ \dfrac{m}{s},$$ $$v_d=2.4\cdot10^{-4}\ \dfrac{m}{s}\cdot\dfrac{3600\ s}{1\ h}=0.864\ \dfrac{m}{h}.$$