Condutcors Help???

Question

In a conductor, the electric field that drives the electrons through the conductor propagates with a speed that is almost the same as the speed of light, even though the drift velocity of the electrons is very small. Explain how these can be true?

Answer 1

it's not true, hence the want to build light operated computers

Answer 2

An external electric field travels at the speed of light -- well not quite, but pretty fast.  There are transmisison line effects -- but we're still talking about maybe 50-70% of the speed of light.  The drift velocity might be mm/sec.

The key is that there is a difference between field speed, and charge speed.  The field is simply the force on the particles -- but the particles have mass so take time to accelerate.  

In a vacuum, a field goes at the speed of light.  If you had a single electron in a vaccuum, it would start from rest, and accelerate using F=ma, and so eventually would reach a large speed.  But initially, because the particle has mass, it takes time to accelerate.  Sort of like asking why gravity travels at the speed of light (it does), yet a falling body goes much slower.

Now, why do the electrons stay slow in a wire -- i.e. why doesn't the speed continue to grow over time (like a falling body does)?  Because in matter, thermal energy causes the electrons to bounce around in random directions -- and they are constantly colliding with othe electrons.  So, although you start to accelerate the electron, it soon stops when it hits another electron, and has to start from zero again.  So it never has enough time to build up speed.  Sort of like how balls in a plinko machine travel much slower than they would if dropped outside.  Or, perhaps a better analogy, how a falling body reaches some steady state due to air resistance (the body slowed by hitting air particles)