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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?

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Related: – Qmechanic Jan 6 '12 at 10:14

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.

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I'm guessing you mean to say: you hear that ELECTRICITY is just another form of magnetism.

Magnets ARE used as generators of electricity - the generator in your car or a hydro-electric dam, etc.

But they are different forms of electro-magnetic energy and are related by the (Faraday-Maxwell) formula: ∇×E=−∂B/∂t. Which basically says: the curled electric field is related to the time varying magnetic field.

Sp when your car revs up, it creates a magnetic field in your generator/alternator, from which an electric field is generated that charges your battery.

Batteries store a static potential electric field. Static, so there is no time variance to create a magnetic field. It's in a different form. Batteries are basically the electrical form. Whereas the motion of magnets (-∂B/∂t) can be used to transform the motion energy into the electric form.

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There is a catch though: You can never get a pure magnetic field by reference frame change from a pure electric field, and vice versa, for

$$F_{\mu\nu} F^{\mu\nu} = \ 2 \left( B^2 - \frac{E^2}{c^2} \right) = \mathrm{invariant}.$$

In other words, starting with a pure electric field, you can only obtain a mixed electric and magnetic field, but never a pure magnetic field.

In this sense, magnetism is not just another form of electricity, though they are closed related.

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In addition to the other answers, you can get an idea of the relationship of the electric and magnetic fields by thinking of an electric motor and a generator as the same thing. When passing current through the coils of the motor, the magnets will spin. On the other hand, if you instead spin the magnets it will create a current in the coils.

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