In some senses the answer to your question is “they’re not different.” Or rather they’re two aspects of the same thing.
A changing electrical field produces a magnetic field, and a changing magnetic field produces an electrical field. So if things line up right, you get a changing electrical field that produces a changing magnetic field that then produces a changing electrical field… the two fields basically generate each other, and you get a wave.
There are other interesting properties like how the fields always produce each other orthogonally (at right angles) and how there are no magnetic monopoles (you can’t have a lone north pole or south pole, they’re always paired) but there are electric ones.
As for “why” you can get into the particles that mediate the fundamental forces, but anything beyond that is less physics and more philosophy.
So electromagnetism has two components, basically – one that is dependent on how many electrons are where (E, electric) and one on how fast the electrons are moving (B, magnetic). The two operate at right angles to each other – if you make a coil of wire with electrons going around it due to the E field down the wire, the B field is at right angles to this. The laws you are looking for are as other respondents have noted Maxwell’s equations.
* So why do magnetic fields pick up ferrous metals? Because if moving electrons make the field then the field makes electrons move.
* So why don’t all materials get picked up by magnets? Because some electrons basically ‘aren’t free enough’ to experience this force – it’s like the rest of the atom shields them.
* So what about permanent magnets? (At ELI5 level? Hoo boy) Electrons are always spinning and this gives them their own magnetic field. Left to their own devices they’ll pair up to make this cancel out to zero, but in ferrous materials they don’t get the chance, leading to materials that can be ‘trained’ to have a standing magnetic field by putting them in a magnetic field for a while.
I realise that a lot of these answers say ‘it just does’ to your questions. That’s honestly the best we’ve got — welcome to physics. Maxwell and those who went before him made a bunch of observations he was able to unify into a theory that explains so much that we can treat it as true – a physical law.
Electric and magnetic fields are intrinsically linked together. This is a fundamental property of existence as we know it. When you have an electric field with oscillations, you necessarily always have a magnetic field with oscillations too. It’s not strictly correct to say that the electric field *generates* the magnetic field–the two are simply always present together.
The reason that we know these waves exist is because they follow from a famous set of equations called Maxwell’s Equations–and physics agrees, we can *see* these waves (literally). These equations were named after James Clerk (pronounced “Clark”) Maxwell, who corrected the equations that existed at the time in order to produce a unified theory of electromagnetism. One of the consequences of his equations is that you can solve them even in empty space–and they predict that, if you change the EM field, it will ripple out like waves. Those waves (necessarily) must travel at one and only one fixed speed: the speed of light.
The difference is whether you’re moving.
A changing electric field induces a magnetic field, and a changing magnetic field induces an electric field.
One way to change an electric field is to move the electric charges around. We call that an “electric current”, and it happens in wires for example. If you were moving along with the current at the same speed, you wouldn’t see the electrons moving, so you’d see the electric field as static and you wouldn’t observe the magnetic field.
An electromagnetic wave can be thought of as an electric field and a magnetic field traveling along together and constantly inducing each other, back and forth. It can also be thought of as a photon, i.e. a particle of light.
So you can create it by running an electric current through an antenna in a controlled way so that it radiates the correct frequency/amplitude/phase/whatever of light to carry the information you’re trying to send. When that wave reaches another antenna, the process happens in reverse (fields induce each other) and you get back the electricity with the same information inside.
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