# Does the voltage difference have an effect on the electrons' speed? [duplicate]

If voltage means the pressure that makes the electrons move from the negative side to the positive one doesn't that mean that the more the voltage there is the faster the electrons move? But the electrons have the speed of light right? does that mean that it will exceed the speed of light if the voltage was big enough.

• Comments are not for extended discussion; this conversation has been moved to chat. Jun 15, 2020 at 9:41
• I looked at the ‘dupe’ question (and even had taken a stab at answering it.) I think the answers that this Q got were much better, and the votes seem to show that (20 votes on mine!) So voting to reopen. Aug 4, 2020 at 15:55

tl; dr: yes, voltage affects electron speed, but not in the way you think.

With no voltage applied, electrons in a conductor rattle around at their Fermi velocity, which while high in its own right (0.81 x 106 m/s for copper), doesn't result in a net electron motion in one direction or another. That is, the vector sum of all the electron velocities is zero.

Applying a voltage to the conductor changes this: the electric field influences the Fermi-speed random motion to have a directional bias from negative to positive. This bias creates a net flow. The speed of that net flow, called drift velocity or $$\v_d\$$, depends on the material's charge density and the current.

That is,

From here:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/miccur.html#c1

We can see that for a given conductor, $$\ne\$$ (charge density) and $$\A\$$ (cross-sectional area) are constant, while $$\I\$$ variable. It follows that $$\v_d\$$ is a variable proportional to current.

That is,

• $$\v_d = \frac{I}{neA}\$$

And by Ohm's law, we can relate voltage to current, and ultimately, $$\v_d\$$:

• $$\v_d = \frac{E}{RneA}\$$

This makes sense: the electrons are being accelerated in a net negative-to-positive flow by the applied electric field, creating the current flow. The greater the the field, the greater the acceleration, and thus the greater the current.

Finally, don't confuse drift velocity with signal propagation. Drift velocity is fairly slow, on the order of cm per second. Signal propagation speed in the other hand is a significant a fraction of the speed of light (0.8C for coax cable, for example). Why? Signals propagate as electromagnetic waves, not as moving electrons.

You didn't specify where the electrons move. We can rip electrons out of their atomic and molecular orbits if we have strong enough electric field. That's done in vacuum electric tubes. Those devices are NOT obsolete. They are still used in high power radar transmitters and X-ray generating tubes. And, of course, many sound subjectivists and musicians like the sound of tube amplifiers. They use the same kind of tubes as in 1950's.

The biggest human built vacuum tubes are the particle accelerators which are used by research physicists.

In vacuum tubes the electrons move faster with higher voltages. One can calculate the achieved velocity by assuming all energy of the electric field is converted to kinetic energy. The thing is presented here https://physics.stackexchange.com/questions/403913/calculating-velocity-of-electrons-in-a-vacuum-tube-read-description

The given formula isn't exact. Part of the speed is lost as electromagnetic radiation which occurs when the speed of the electrons change. Another inaccuracy is ignoring Einstein's relativity. It must be taken into the account when the speed is a substantial part of the speed of light, say 30m/us or more. Relativity shows that the speed of light cannot be achieved , no matter how high voltages we have.

In metals the sheer number of electrons in very loose orbits which allow electric current is very high. Any practically achievable currents need in normal wires so small percentage of the available easily movable electrons that the velocity of the electrons can be very slow, very likely less than one millimeter per second. Se this for more details: https://en.wikipedia.org/wiki/Drift_velocity#Numerical_example

The signals occur actually in the fields outside the metal; that's a wave, just like of the radiowave, but metal wires (actually the electrons in the metal) direct it to the load. Very small part of the energy of the signals (or as well of the electric power)travels inside the metal conductors, the major part travels outside the metal but to the direction of the wires.

In high frequencies we meet wire constructions which tend to lose some energy to the space around the wire. Antenna builders try to maximize that effect and manage the radiation direction. Transmission line builders try to minimize it.

• "Sound subjectivist" is the nicest name for an audiofool I've heard so far :-) Jun 15, 2020 at 14:03

The best way to think about this question is to get very precise about the definition of the word "move". Here are three different ways in which the electron moves:

1. The electron orbits around the nucleus of its atom. This happens at a very fast speed, which can be near the speed of light for some atoms. https://www.quora.com/What-is-the-speed-of-an-electron Edit: as wizzwizz4 points out, this isn't really true -- thinking about the "speed" of an electron within the atom is a fundamentally incorrect model. See for example this answer here: https://chemistry.stackexchange.com/a/26505.
2. The electron moves from atom to atom within the conductor. If there is no voltage field present, then this motion will be random with a long-term average of zero movement (i.e. in the absence of a voltage field, the electron will probably end up back where it started). This occurs at the Fermi velocity. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html
3. In the presence of voltage, this random movement of the electron will also have a long-term trend. (Over time, the electron will end up farther down the wire than where it started.) This is called the "drift velocity", and this is the speed you're really asking about in your post. https://en.wikipedia.org/wiki/Drift_velocity

As you can see from the Wikipedia article, the drift velocity is really pretty slow (as others have pointed out) and can be derived from the current (and properties of the conductor).

• The electron doesn't whizz around the nucleus of its atom; its position-momentum is such that the electron is in an orbital around the atom. Those Quora answers are mistaken or misleading. Jun 14, 2020 at 21:02
• @wizzwizz4 True enough. Edited. The Bohr model is fundamentally incorrect but has great intuitive appeal. This reminds me of a favorite old quote, something about how the process of teaching physics is a process of telling smaller and smaller lies. Jun 14, 2020 at 21:36

Electrons have mass. That's why they never reach the speed of light.