Question 413: Current Electricity

Question

The number density of free electrons in copper is nearly $$8 	imes 10^{28} \mathrm{~m}^{-3}$$. A copper wire has its area of cross section $$=2 	imes 10^{-6} \mathrm{~m}^{2}$$ and is carrying a current of $$3.2 \mathrm{~A}$$. The drift speed of the electrons is ___________ $$	imes 10^{-6} \mathrm{ms}^{-1}$$

Accepted Answer

Using the formula:
$ I = n e A v $
where $I$ is the current, $n$ is the number density of free electrons, $e$ is the charge of an electron, $A$ is the cross-sectional area of the wire, and $v$ is the drift speed of the electrons.
We can isolate $v$ to find:
$ v = \frac{I}{n e A}$
Substituting the given values:
$ v = \frac{3.2 \, 	ext{A}}{8 	imes 10^{28} \, 	ext{m}^{-3} 	imes 1.6 	imes 10^{-19} \, 	ext{C} 	imes 2 	imes 10^{-6} \, 	ext{m}^2}$
This simplifies to:
$ v = \frac{3.2}{16 	imes 1.6 	imes 10^3} \, 	ext{ms}^{-1} = 125 	imes 10^{-6} \, 	ext{ms}^{-1} $
So, the drift speed of the electrons is indeed $125 	imes 10^{-6} \, 	ext{ms}^{-1}$.

Current Electricity

The number density of free electrons in copper is nearly $8 \times 10^{28} \mathrm{~m}^{-3}. A copper wire has its area of cross section =2 \times 10^{-6} \mathrm{~m}^{2} and is carrying a current of 3.2 \mathrm{~A}. The drift speed of the electrons is ___________ \times 10^{-6} \mathrm{ms}^{-1}

Choose the correct answer: