If you were to use a spacecraft built of copper in Earth's magnetic field, could you produce enough energy to propel yourself?
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.