31st January 2007 - 04:09 AM
if anyone could help me, i would greatly appreciate it! I'm relatively new to physics and am struggling a little bit with a new topic... we just finished electrostatics and are now moving on to electricity.
the homework problem reads:
"A 200 km long high voltage transmission line 2 cm in diameter carries a steady current of 1000 A. if the conductor is copper with a free charge density of 8.5 x 10 to the 28 (not sure how to do exponents on the computer) electrons per cubic meter, how long (in years) does it take one electron to travel the full length of the cable?"
knowing my level of physics expertise, this very well be a simple problem, but i could really use some help understanding what exactly is going on!
thank you in advance to anyone who can help me!
1st February 2007 - 03:56 AM
This is fairly simple if you think about it in the right way. Suppose an electron enters the wire at one end, and suppose that all the electrons flow along through the wire like water through a pipe. Then this electron cannot come out the other end until all the other electrons that are ahead of it in line have come out.
How many electrons are there ahead of it? Since it just came into the wire, EVERY electron in the wire is ahead of it.
How many is that? You know the number of electrons per cubic meter, so if you multiply by the number of cubic meters of wire volume, you'll get the total number.
What is the wire volume? It is a cylinder, so the volume = length * (pi * r squared). (BTW you can write exponents like this: r^2, 10^28, etc.). You have the length, and of course the radius is half the diameter. Be sure to convert them to meters first.
Now you know how many electrons need to come out before our particular one can come out. But how long will that take? Since quantity = rate * time, and you have quantity and want time, you need to find rate:
How how many electrons come out each second? The current (1000A = 1000C/s) tells how many Coulombs of charge come out each second, and electrons have a charge of 1.609 * 10^(-19) C/e. Therefore if you divide the current by this charge, you will get (C/s) / (C/e) = e/s, which is the number of electrons per second.
Now you're basically done, because you have the quantity and the rate, so you get the time by quantity/rate. This time will be in units of seconds.
How many years is that? 1 year = 31,556,952 seconds, so divide by this number to convert to years. That's the answer.
Discussion: The point of this problem is to show you that it takes a REALLY long time for electrons to work their way down a wire. This should be puzzling, because your light turns on right away when you flip the switch, not several hours later. What is happening is that when you start pushing electrons in one end of the wire, they immediately push the ones ahead of them out the other end, basically because they repel each other. It's like water in a pipe: If the pipe is full of water already, then as soon as you push a little more water in one end, since there is not room for any more, some water must IMMEDIATELY come out the other end. Of course, it's not the SAME bit of water you just pushed in, but all water looks alike, and so do all electrons. The water you pushed into the pipe just now will come out the other end sometime later after it works its way down the pipe, but you don't have to wait for that particular bit of water to come out the other end, because the water that was already near the other end will come out immediately. The electric current works the same way.
Hope this helps!
2nd February 2007 - 12:07 AM
Thank you so much! It helped quite a bit!