Question

Over and over I'm getting into the same trouble, so I'd like to ask for some help.

1. I need to solve some basic electrodynamics problem, involving magnetic fields, moving charges or currents.
2. But I forgot all this rules about "where the magnetic field should go if the current flows up". I vaguely remember that it about hands or fingers or books or guns, and magnetic field should go somewhere along something, while current should flow along something else... But it doesn't help, because I don't remember the details.
3. I do find some very nice rule and use it. And I think "that one I will never forget".
4. ...time passes...
5. Go to step 1.

The problem is that you have to remember one choice from a dichotomy: "this way or that way". And all the mnemonics I know have the same problem -- I got to remember "left hand or right hand", "this finger or that finger", "inside the book or outside of the book".

Maybe someone knows some mnemonics, that do not have such problem?

Answer 1

if the electric field is a vector with an arrow, then the magnetic field is fundamentally not a vector: instead, it is an antisymmetric tensor with two indices, determining an "oriented two-plane".

The latter carries the same information (3 different components) as a vector, and there is a convention given by the right-hand rule to switch from one to the other. A derived and related rule also determines the magnetic field of a solenouid and other things.

Clearly, the convention to switch from the antisymmetric tensors to vectors could have been the other way around, too. So one has to remember something to know the convention; one can derive many things but not conventions. I agree that remembering the right hand operations is simple, especially because the word "right" also means "correct" and because the right-wing political opinions are the right ones while the left-wing political opinions are those that are left over.