# Currents and the Speed of Light

Why is it that currents don't flow at the speed of light, but rather significant ratios of the speed of light. I don't have any formal reasoning as to why they would flow at the speed of light-I just feel as if it would make sense. That being said, the fact that they do move at near the speed of light is also peculiar to me. Lastly, if you have current and area determined, can you figure out the velocity of the charges? I suppose you would also need to know how big the charges are. I just have no intuition as to how to go about analyzing the speed of current in some given wire.

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As Lagerbaer notes, current are typically very slow. Signals move at a significant fraction of $c$. –  dmckee May 15 '13 at 5:08
Possible duplicate: physics.stackexchange.com/q/17741/2451 –  Qmechanic May 15 '13 at 6:19
Resistance of a wire. Some materials are known to have higher resistivity. They are charges moving. Current is the rate of flow of charges. Those charges still have mass. Anything that has mass cannot travel at the speed of light unless it has infinite energy. Unless the Electromotive force is extremely high, probably near infinite.. I think only then will it be possible? –  owlp May 15 '13 at 8:49

A current is nothing than charged particles moving. Since those charged particles also have a mass, it follows that they cannot possibly reach the speed of light.

In a real material that conducts electricity, the average net velocity of charges is actually very, very low, because they bump into atoms all the time, which basically sends them flying off in random directions until they get acellerated again.

The key word that you'd be interested in is drift velocity.

EDIT: However, something is quite fast (almost speed of light), and that's the propagation of the electric field associated with the current (see comments).

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... and the electric potential generated by the moving charge travels through the conductor at significant fraction of the speed of light. –  Brandon Enright May 15 '13 at 4:50
@BrandonEnright's comment is key here - when you flip a light switch, you don't have to wait for the electrons near the switch to travel to the light-bulb. The electric field is affected all the way throughout the circuit at a much faster speed than the electron drift speed. –  kleingordon May 15 '13 at 5:32
I never made a claim to the contrary; I was just talking about current :) –  Lagerbaer May 15 '13 at 5:41
So the 'electrons' in the wire aren't really moving? It seems as though the electrons would move faster in the absence of current flow than in its presence (.00028 m/s isn't very fast). It's amazing how we can send signals when the actual electrons are simply oscillating about their initial positions (in alternating current). It's kind of like vibrating one end of a very long rod, but having the signal travel much faster than any individual piece (the signal I believe travels at the local speed of sound?) The electrical circuit is then simply an modern version of the tin can telephone. –  Greg May 15 '13 at 6:15
@Greg "It's amazing how we can send signals when the actual electrons are [...]" Firstly the electrons do exhibit a net movement, and though they move slowly there are a lot of them doing it, but perhaps more importantly you should be treating the electromagnetic fields are first class objects that are just as important as particles and changes in those fields propagate quickly. –  dmckee May 15 '13 at 13:36

Current is movement of charge. In conductors that's usually electrons doing the movement (flowing). One of the things keeping them from moving quickly is that they bump into each other and all the metal atom nucleus's constantly. Secondly, because your battery isn't sufficient, it creates a very limited potential difference. Even if the electrons never bumped into any nucleus, by energy conservation $\frac{mv^2}{2} = eV$ the electron speed $v$ will be much less than the $V$ potential, compared to the speed of light. Also, then there'll be other relativistic effects. relativistic effect means , that as you will move faster , it will require more energy to further increase your speed . If you take a very high potential Battery .

In the case of an induced EMF circuit , however, this energy conservation relation won't hold as now $\vec E$ / $\vec B$ aren't conservative , so , here relativistic effects and resistance only will be the reason why current can never attain speed of light .

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You should elaborate on "there'll be other relativistic effects". I can't think of any relativistic effects for "normal" voltage and current levels in typical everyday conductors. –  Brandon Enright May 15 '13 at 6:45
Regarding your edit and explanation "it will require more energy to further increase your speed . If you take a very high potential Battery" is there ever a (reasonable) case where drift velocity or thermal velocities approach levels where relativistic effects matter? I'm almost certain the conductor would melt long before the electrons had relativistic velocities. –  Brandon Enright May 15 '13 at 6:51
@BrandonEnright Yes, I said even if all of this theoretically happens the melting point of the conductor isn't a theoretical restriction but rather a practical one . –  nonagon May 15 '13 at 6:53