# Why does current travel at speed of light rather than speed of sound?

• dEdt
In summary, the explanation for the quick turn-on of a light bulb after you flip the switch is that a "wave" or disturbance is created, which travels the short distance to the light bulb almost instantaneously. However, this wave does not travel at the speed of sound, and is instead slowed by the weight of the electrons.f

#### dEdt

Here's how I understand the situation: when an electrical current is running through a wire, the individual electrons are moving very slowly. The reason that a light bulb turns on so quickly after the switch is closed, then, is because as the electrons near the switch start moving, they push on the electrons nearby, which push on the electrons nearby, and so on: a "wave" -- or a disturbance of some sort at least -- is created, which reaches the light bulb almost instantaneously.

But don't disturbances of this sort travel at the speed of sound (in the material)? Why does this disturbance travel so much faster? I don't think it's because the electrons are lighter: the difference in speed seems too great.

The E field from each electron pushes the one in front of it. A change in an Electric field travels at c. Good question though.
Since we are in a material it won't quite be c. it will be a little less like when light travels slower in glass.

The E field from each electron pushes the one in front of it. A change in an Electric field travels at c. Good question though.
Since we are in a material it won't quite be c. it will be a little less like when light travels slower in glass.

Isn't that exactly how sound gets transmitted? The E field from each atom pushes the one in front of it?

If it's a classical effect, then I would guess it is indeed because of the weight difference. Although I agree that that does sound suspicious because the weight difference doesn't seem that great. However, I did hear that the electical signal doesn't really travel at the speed of light, but instead much slower.

I would go further though and go ahead and guess that quantum effects play a part in this more than anything.

Electrical signals are not carried by the mechanical energy of moving electrons. They are carried by...the electrical energy.

Sound is mainly transmitted by moving atoms, not electrons. Atoms are heavy and slow, and there is no global field moving them.
Electric currents depend on electric fields - those change with the speed of light (or a bit slower in materials), and all electrons get moved by this electric field.

Electrical signals are not carried by the mechanical energy of moving electrons. They are carried by...the electrical energy.

This is actually a very good, albeit terse, answer. Just to expand on it, the effect of a conductor (i.e. the wire) is to guide the electromagnetic disturbance (be it a wave, a pulse, etc.). Since you have an EM disturbance, it propagates at the speed of light (actually the speed of light divided by the index of refraction, which still tends to be pretty fast).

Now, as the EM disturbance propagates "very far" away along the wire, the electrons in that portion of the wire see the newly arrived electric field and begin to move. This is the reason that current also propagates at the speed of light (divided by the index of refraction). Again, as the electric field propagates, it move electrons wherever it moves to. To a first (and very good) approximation, the electrons don't even interact with each other -- so there's no "speed of sound" issues that you originally brought up.

You may have already done this exercise already, but the current density is given by
J = q n v
where J is the current density (A/m^2), q is the elementary charge, n is the number of electrons per unit volume, and v is the average velocity of a single electron. Take a normal household current and use the atomic density of copper while assuming that one copper atom contributes one free electron. Now calculate the velocity v. You'll find that the electrons literally move at a snail's pace. Yet the current move at the speed of light!

Electrical signals are not carried by the mechanical energy of moving electrons. They are carried by...the electrical energy.

I guess where I (and possibly OP?) are getting confused is that I thought, ok, the generator or whatever uses its magnetic field to push on the electrons in its vicinity (kind of like a pump pushes water that it directly contacts). Then those electrons move, causing their magnetic field to move, which pushes the electrons next to them...and so forth.

But now I'm led to understand that the generator uses its magnetic field to push ALL the eelctrons in the wire? Is this correct?