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I've been reading this website: www.physics.wayne.edu/~apetrov/PHY2140/Lecture8.pdf to learn how fast an electron moves in a circuit.

On page #8, #9 and #10 It says to take the Cross-sectional Area of the wire, The current, The density, The Charge and the electrons^3

Area-                 3.14x10^-6 ( 2mm thick wire = 3.14 × (0.001 m)^2 = 3.14×10^−6 m^2 = 3.14 mm^2)
Current-              10 I
Density of copper-    8.95 g/cm^3
charge of 1 electron- 1.6x10^-19
electrons^3-          8.48x10^22 = ( 6.02*10^23 mole * 8.95 g/cm^3 * (63.5 g/mole)^-1  )

Total: 10 / 8.48x10^22 m^3 * 1.6x10^19 * 3.14x10^-6 m^2 = 2.48x10^-6 m/s

But they say that with 2.48x10^-6 m/s It'll take the electrons 68 minutes to travel 1 meter, How is that possible?

When I calculated that equation I end up with 5.9245283e+35, Then when I try to calculate again to get 68 minutes to travel 1 meter I can never get it right.

I'm not the best at math, The m's confused me. What am I missing ?

hello moto
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3 Answers3

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The calculation on page 9 of the PDF is incorrect because of the author's confusion mixing meters and centimeters combined with a numerical error. (Sad!) The correct calculation of the drift velocity for the input values given is

$$v_d=\frac{I}{nqA}=\frac{10.0\,\text{C/s}}{(8.48\times 10^{28}/\text{m}^3)(1.6\times 10^{-19}\,\text{C})(3.00\times 10^{-6}\,\text{m}^2)}=2.46\times 10^{-4}\,\text{m/s}$$

so the time to go one meter is

$$\frac{1\,\text{m}}{2.46\times 10^{-4}\,\text{m/s}}=4065\,\text{s}=67.75\,\text{min}.$$

You might want to find a better site for studying this subject.

G. Smith
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It's because of drift velocity of electrons. Though the electromagnetic disturbance propagates at somewhat near the speed of light, the actual velocity with which the electrons move is much lower because of collisions with the ions in the lattice and random thermal motion.

The electrons can't move fast because they are continuously being slowed down by collisions and hence aren't moving through free space.

When a voltage is applied across a wire, the electrons move in response to the electric field generated and have a net movement in the direction of the field with very small velocities.

user8718165
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When an electric current is established in a 1 meter wire, it is NOT every electron travels 1 meter from one end to the other end. It is all electrons simultaneously move at very slow speed of $10^{-6} m/s$.

This $10^{-6} m/s$ has nothing to do with the travel speed of electric current in the wire. The speed of current corresponds to how fast can very far apart electrons get ordered to move together, which is very fast, close to the speed of light. Though electrons move slowly, they get ordered very fast under voltage.

Jinchen
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