[Physics] Understanding the relationship between electricity and magnetism

Question

I keep on hearing that magnetism is just another form of electricity and vice versa. If that's the case why can't we use magnets as batteries, and why aren't my batteries magnetic?

Answer 1

One way to interpret the statement "electricity is another form of magnetism" (or vice versa) is through special relativity. If I look at a classical stationary electric charge, it sets up a purely electric field - the Coulomb field, which is responsible for generating the phenomena of static electricity. However, if I now look at this same electric charge, but from the standpoint of a reference frame which is moving with respect to it, what I now see from my new point of view is a moving electric charge, in other words an electric current. An electric current sets up a magnetic field (Ampere's law).

Thus we find the same physical source generating a field which looks like either a magnetic field or an electric field depending upon how you look at it. This transformation between electric and magnetic fields is perfectly described by the Lorentz transformations of special relativity.

Returning to the specifics of your question, permanent magnets generate their magnetic field through two main mechanisms - firstly there is the orbital motion of electrons around the nucleus. Since the electrons are charged, this is equivalent to an electric current and sets up a magnetic field. Secondly, there is the spin of the electrons themselves - this again creates a magnetic field (although it is tempting to think of the electron as a little spinning charged object of finite size, this would be incorrect, the proper description being a quantum mechanical one). The net effect is that the atoms behave as tiny magnets.

In ferromagnetic materials the motion has the right "collective" properties such that the atoms, which behave like a tiny magnets, are able to align their magnet's directions (in local units called magnetic domains) to provide a large magnetic field. However (1) the orbital motion of the electric charge in the atoms is cyclical, and (2) the spin of the electron doesn't move the charge from one place to another whereas what you'd need for a battery is a movement of charge which results in separation of positive and negative charge, to make available at the terminals. Thus permanent magnets can't function as batteries.