Re: Questions about Space Elevators

If you don't feel like reading this whole answer, I can tell you right 
away that considering all known and proven technology, a space elevator 
would probably not work and definitely not be profitable.
1- The cable length would depend on a few variables.  One, how far out you 
wanted to go, obviously.  If the elevator was intended to carry loads to 
orbital platforms, 100,000 km would be appropriate.  However, if the 
intention was to only reach technical space, that is, as close to earth as 
you can get while still being in "space," only a few thousand kilometers 
would be needed.  But it would also depend on whether the cable would go 
straight down or not.  I'll get into that later.
2- Of course you could power the elevator with an electrodynamic cable.  
Alternating current can travel long distances without losing very much 
power, so it would be possible.
3- This raises issues of tethered orbiting, read on about this after the 
last answer.
4- It could carry, technically, any load you designed it to, like any 
elevator.
Ok, now onto the tricky stuff.  There are many, many problems with the 
design of an object orbiting the Earth, but even more problems to consider if 
the object is to be connected to Earth as well.  
First of all, if it did not have a geostatic orbit, the tether would slowly 
be wrapped around the Earth.  This is a really weird idea, and it wouldn't 
actually happen this way.  What would really happen is that it would be 
broken and ripped by all the things moving and flying around in the 
Earth's atmosphere, and it would fall to the surface.
If it did have a geostatic orbit, it would be very tricky to maintain it.  
The Earth spins at approximately 1,000 miles per hour, and things orbiting 
geostatically must have this speed as well.  As you may know, in space, 
there is little to slow down something in motion, so very little maintenance 
is required to keep satellites and such in geostatic orbit - they just keep 
going (although the Earth's gravity does slowly pull them in, so they must 
either be boosted back occasionally or allowed to enter the atmosphere and 
burn up).  However, a space elevator would not be free-floating, it would 
be attached to the ground.  This means that not only would it be subjected 
to the pull of gravity on its own mass, but on the entire cable as well, 
which would weigh tens or even hundreds of thousands of tons.  Unless 
constant thrust was provided, the elevator would come crashing down.  Not 
only that, but to keep it in step with the rotation of the Earth, one 
would need to provide not only the thrust to accelerate the elevator to 
the proper velocity, but the entire length of the cable as well.  This 
would almost undoubtably cause the cable to lag behind, and bring the 
elevator closer to the Earth.  So, the cable would be in an arc shape 
instead of a line, and even more would be needed to keep the elevator at a 
proper height.  And that's only the tip of the iceberg.
As you can see, a space elevator, by modern standards is not possible.  
Even if it was somehow built, whoever did build it would go broke very 
quickly.  Sorry to bear the bad news, but those are the facts.