# Can a Planet's Electromagnetic Field Be Strong Enough for Wireless Electricity (Induction)?

Wikipedia states:
"Electromagnetic or magnetic induction is the production of an electromotive force (i.e., voltage) across an electrical conductor in a changing magnetic field."

This one sentence has baffled me and raised more questions than answers. As I would strongly prefer to not have to learn an entire field of science, I decided it was time to post a question on the topic.

Is it possible to build a device capable of charging electronic devices by using the planet's electromagnetic field as an energy source? Is there any situation in which this might be possible, even if unlikely?

Good answers will tell me why or why not this is possible, and a "electromagnetic induction for dummies" rundown would be appreciated as well.

Bonus points to someone who can calculate how strong of an electromangetic field a planet would need to make this possible. (if even possible)

• The keyword is "a changing magnetic field": a variation of the magnetic flux through a conductor loop induces an electric current; a constant magnetic flux induces no current. A planet's magnetic field is static, or at best it varies very slowly. By itself it won't induce a current. But, if you take a loop of wire and rotate it in Earth's magnetic field you will get an electric current; the catch is that the electric energy comes from the mechanical work of rotating the wire loop. Sorry, but no: the energy does not come from the magnetic field. – AlexP Oct 3 '19 at 1:08
• I'm thinking that a planet with a magnetosphere strong enough for wireless (broadcast) electricity would be uninhabitable by any creature requiring electrical impulses for brain and neural functions (aka, humans). Food for thought. – JBH Oct 3 '19 at 3:54

Electromagnetic or magnetic induction is the production of an electromotive force (i.e., voltage) across an electrical conductor in a changing magnetic field.

This is correct, but the operative word here is "changing". Specifically, Faraday's law states

$$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$

If you're not familiar with vector calculus, fret not! This equation basically says that the "twistiness" of the electric field is directly proportional to how quickly the magnetic field is changing. But twistiness of the electric field can set up a voltage in a conducting loop (well, technically it's an EMF, not a voltage), since a twisty electric field can push charged particles all the way around the loop.

But as I alluded to before, the problem comes from the fact that we need our magnetic field to be changing for this to happen-- if it isn't, the right hand side is zero and the electric field has no twistiness, meaning no EMF to push charges through our circuit. Now, while the Earth's magnetic field does change over time, it does so very slowly, meaning that even with a very large loop you wouldn't be able to power much.

Now, you might ask "well, the Earth might not have a field that varies quickly enough to do this, but what about other planets?" Sadly, the answer is still that it's infeasible. You see, magnetic fields have a property somewhat like inertia, in that they don't like to change. In fact, if an object has a changing magnetic field, Maxwell's equations predict that the object will act like an antenna and radiate away energy. As a consequence, most planets have relatively stable magnetic fields-- if the magnetic field is rapidly changing, it eventually slows down as energy is expended.

There are a few examples of astronomical bodies with high magnetic fields that quickly change, but they tend to be poorly suited to life and short lived. Some of the most extreme examples are magnetars, which are neutron stars with magnetic fields about 15 orders of magnitude stronger than Earth's. By virtue of having strong fields that vary quickly thanks to high rotation rates, they emit a ridiculous amount of radiation. The fields tend to decay by about 10,000 years, which is the blink of an eye by geological standards.

• +1 for comparing vector calculus to twistness of vectors haha. Very nice "dumbing down" :) – KingDuken Oct 3 '19 at 4:52
• By no means an actual practical solution, but would a planet with enough rotational inertia and strong enough magnetic field be usable as a giant DC electrical generator? Methinks the OP wants a planet killing source of energy beside fossil fuels XD – vinchenso Oct 3 '19 at 6:33