If you were to use a spacecraft built of copper in Earth's magnetic field, could you produce enough energy to propel yourself?
4$\begingroup$ No. OTOH, if you have an alternative energy source, you might be able to propel yourself against the magnetic field. Although, due to some engineering and physics caveats, the achievable thrust is really minuscule. $\endgroup$– SF.Nov 9, 2016 at 23:32
$\begingroup$ Is this question about extracting energy from the magnetic field, or about generating thrust, using energy from elsewhere? $\endgroup$– VoracAug 23, 2017 at 12:18
There is a question on the World Building Stack Exchange relevant to this. The consensus there seems to be no you can't.
This answer in particular by user Schwern seems to have the answer to your question. Note that the original question was about power generation for a living space in Jupiter's orbit, but it answers your question too.
Jupiter has an enormous magnetic field, and your house is moving through it. You could wrap some wire around a coil and extract electrical energy from this field! Brilliant!
...except by doing so you're creating an oppositely charged magnet which Jupiter's magnetic field draws in creating a drag on your house's orbit. You're mortgaging your house's orbit for electricity. This is a theme.
You could kick the electro-magnet out into space. Then it will be in its own orbit. It would send the energy back to you with a laser (also a theme) and eventually crash into Jupiter.
6$\begingroup$ The answer quoted states that orbital velocity and power are interconvertible, which means you have utterly misunderstood the applicable conclusion. If you can draw power from the magnetic field by slowing down your orbit, it stands to reason that by putting power in, you can speed up your orbit. $\endgroup$ Oct 11, 2017 at 19:32
There are magnetic fields everywhere in space. If it were possible to use them for propulsion the achievable speeds would be incredible. Place two magnets close to each other and see how fast they come together.
2$\begingroup$ Magnetic force rapidly falls off with distance (proportional to the third power of distance), so the behavior of magnets up close is no indication of what a magnetic propulsion system will do. $\endgroup$– HobbesAug 23, 2017 at 7:43
$\begingroup$ You should try to demonstrate this on Earth using its magnetic field. Good luck, you will need it. Moving a compass needle does not count, try a toy car. $\endgroup$– UweAug 23, 2017 at 10:10