Exploring the Effects of Rapidly Changing Voltages on a Long Wire

[dashkin111]

What would happen if say, there was a really long wire.. say 186,000 miles or so long. You apply a voltage on one end, and on the opposite end less than a second later you apply another voltage. And you keep going back and forth. Would the net current effectively be zero? How would the electrons behave qualitatively?

I'm just curios.

 

[chroot]

The change you introduce in the electromagnetic field at one end of the wire (which motivated electrons to move through the wire) will take about one second to propagate to the other end of the wire.

No current flows through the wire as a whole until the change in the electric field has propagated its entire length.

- Warren

 

[dashkin111]

So the electromagnetic field as a whole would "cancel out"?

 

[chroot]

If you continually change the potentials at each end of the wire, you'll get waves which propagate down the wire in both directions. The potential will be changing at every point in the wire over time in a complex way that depends on exactly how you're changing the potentials at the ends.

- Warren

 

[dashkin111]

Interesting... and I'm guessing if I curled it up into a big solenoid the field through the middle would move back and forth with the changing e&m waves?

 

[chroot]

That's correct, but it would be hard to analyze. One of the assumptions made about wires that aren't light-years in length is that current flows equally through any cross-section. This is only true, of course, when the electric field is uniform throughout the wire's length. When the wire is astronomically long, the electric field takes significant time to propagate through it, and the current will not be the same in every cross-section.

- Warren

 

[dashkin111]

Cool, but do suppose you could get a similar effect with a shorter wire/coil by rapidly(VERY rapidly) changing the voltages at each end, or would that be unrealistic to ever attempt?