Understanding Energy Conservation in Magnetic Fields and Current-Induced Wires

[scienceteacher]

When current is introduced inside of a wire it creates a magnetic field...also generating a magnetic potential energy for any nearby magnetic fields. How is energy conserved in this process?

Similarly... I read that a large 13 mile wire was put into orbit around Earth's magnetic field inducing a current. How is energy conserved??

Thanks all!

 

[Bob S]

A 1 meter length of a 1-mm diameter copper wire has an inductance of about 1.5 microhenrys. E = (1/2) L I^2

 

[Andy Resnick]

When current is introduced inside of a wire it creates a magnetic field...also generating a magnetic potential energy for any nearby magnetic fields. How is energy conserved in this process?

Similarly... I read that a large 13 mile wire was put into orbit around Earth's magnetic field inducing a current. How is energy conserved??

Thanks all!

The induced field should not act on other, existing, magnetic fields- linear superposition holds for most cases.

If the induced magnetic field acts on ponderable matter, the energy acquired by the matter (by aligning magnetic dipoles, for example) is lost by the magnetic field (at some efficiency). This will in turn act on the original current. Since the magnetic field is generally smaller than the electric by a factor 1/c, the perturbation can usually be neglected (but careful measurements can probably detect).

The experiment you speak of was the Tethered Satellite System

http://science.ksc.nasa.gov/shuttle/missions/sts-75/mission-sts-75.html

Unfortunately, it was wildly unsuccessfull.