How does an ElectroDynamic Tether (EDT) clear space debris? Earlier today (9 December 2016), the Japan Aerospace Exploration Agency (JAXA) launched their Kounotori Integrated Tether Experiments (KITE) into orbit.  What I understand from the description is that it will have a 20 kg weight at the end of a 700 m tether.  If I understand correctly, the current mission is one of measurement (of induced current and voltage) rather than an attempt at actually clearing space debris.  
However, the technology is touted as a promising candidate to deorbit space debris at low cost.  In doing some searching, I have not yet found a clear explanation for how that would work.
My question: How would this actually work for that purpose?
 A: Clearing (large) debris objects with current sats would take a large amount of fuel.  Enough that doing more than one or two is unlikely to be possible.  If you carried more fuel, doing the first one is more expensive (in fuel terms).
Electrodynamic tethers allow you to take power and electrons and use that to "push" against the earth's magnetic field for propulsion.  With solar panels, you can now (theoretically) generate low levels of thrust indefinitely in low earth orbit and zero propellant.
This could allow enough manueverability to catch up to some deorbit candidates, attach or otherwise grab, then thrust again until close to deorbit.  Then raise back up and repeat.
See also:
http://erps.spacegrant.org/uploads/images/2015Presentations/IEPC-2015-301_ISTS-2015-b-301.pdf

I don't understand how it affects the debris which is presumably in some close orbit

KITE doesn't.  From the PDF:

Primary objectives of KITE are to obtain data on
  the fundamental characteristics of the original EDT components

In other words, a full-up deorbit system would need lots of things (some method of control, approach, and capture of debris included).  But KITE was only designed to test the tether and its ability to provide zero-fuel thrust.  Assuming that portion becomes more viable in the future, the additional problem of capturing and de-orbiting debris would need to be worked on.
A: 
The system comprises a long tether which is electrically conductive with devices for electron emission and collection. The system generates drag for reentry of debris by inducing an EMF along the length of the tether, caused by crossing Earth's geomagnetic field. 
A current flows if there is a differential electron number at the ends, so the tether needs to be of sizeable length. 
So far, so good.
The 
interaction between the geomagnetic field and the 
tether-current generates J×B force against the orbital 
motion. 
No, I don't 100 percent follow that last part either, except to say I would guess that the debris has collected it's own charge over the time it's been up there.  I will amend this post if I think of a better idea.
Nope, I am wrong re above. Version 2 is that they  create a plasma by ejecting electrons around the debris and slowly  slowing it down by the constant flow of electrons against it.
The current along the wire opposes that, and slows the craft down until it starts to feel the atmosphere,  then that's that for the debris.
