Question 414: Current Electricity

Question

A current of $$2 \mathrm{~A}$$ flows through a wire of cross-sectional area $$25.0 \mathrm{~mm}^{2}$$. The number of free electrons in a cubic meter are $$2.0 	imes 10^{28}$$. The drift velocity of the electrons is __________ $$	imes 10^{-6} \mathrm{~ms}^{-1}$$ (given, charge on electron $$=1.6 	imes 10^{-19} \mathrm{C}$$ ).

Accepted Answer

The drift velocity $v_d$ can be found using the formula for current $I$ in a conductor:
$I = nqAv_d$,
where:
$n$ is the number density of free electrons (number of free electrons per unit volume),
$q$ is the charge of an electron,
$A$ is the cross-sectional area of the conductor, and
$v_d$ is the drift velocity of the electrons.
We can rearrange the above formula to solve for $v_d$:
$v_d = \frac{I}{nqA}$.
Given that $I = 2 \, 	ext{A}$, $n = 2.0 	imes 10^{28} \, 	ext{m}^{-3}$, $q = 1.6 	imes 10^{-19} \, 	ext{C}$, and $A = 25.0 \, 	ext{mm}^{2} = 25.0 	imes 10^{-6} \, 	ext{m}^{2}$, we can substitute these values into the formula to find $v_d$:
$v_d = \frac{2}{(2.0 	imes 10^{28})(1.6 	imes 10^{-19})(25.0 	imes 10^{-6})}$
$v_d = 25 	imes 10^{-6} \, 	ext{ms}^{-1}$.
Therefore, the drift velocity of the electrons is $25 	imes 10^{-6} \, 	ext{ms}^{-1}$.

Current Electricity

Choose the correct answer: