Electrodynamic Tether experiement

[shubhankar1]

I was reading about the electrodynamic tether experiments in low Earth orbits to generate electricity. I had a doubt regarding the mathematics that went behind calculating the emf across the tether. I read further and i realized they use the equation ε=Bvl, but the problem with this is that the B is not constant throughout all points in orbit. So how do you find the emf across the tether in this case where there is relative motion with velocity v and B changes at all points in the path of the wire?

 

[mfb]

Integrate over the length of the wire.

$\epsilon = \int_a^b B(s) v(s) ds$