Right Hand rule-Why is it possible

[wolfhound25]

Homework Statement

I understand that the right hand rule is a convention to give the movement of charged particles around a current carrying wire, but why is it possible to have a standard convention? Why can't the charge particles move either way? Why does the movement of particles in that direction cause that specific magnetic field?

Homework Equations

The Attempt at a Solution

 

[paisiello2]

By fiat.

 

[Merlin3189]

"I understand that the right hand rule is a convention to give the movement of charged particles around a current carrying wire,"
I'm not sure that this is what a right hand rule says.
If charged particles are moving near a current carrying wire, they will experience a force due to the magnetic field around the wire. The direction of that force will depend on the direction in which they are already moving. The force will then modify their motion, but I don't see any simple RH rule for it.

Are you perhaps thinking of the magnetic field caused by the wire?

I wouldn't call the right hand rule "a convention". It is just an aid to remembering what happens.
A convention is usually an arbitrary decision, like taking "up" as the positive direction in a calculation, or saying current flows from positive to negative, or magnetic field is directed from a N pole to a S pole. Once the arbitrary decisions about the direction (sense) of current and field had been made, then the connection between them is determined by nature. That's the way it is.

The magnetic field caused by movement of charge is always in this direction - that is an experimental observation. We could not just say it was the opposite way - we would just be wrong! We just have to remember that is the way it is.

 

[haruspex]

My answer is more or less the same as Merlin's, but perhaps with a different emphasis.
Physicists define positive charge arbirarily and direction of magnetic field lines arbitrarily. Having mode those assignments, the right hand rule is an observed fact connecting them.
(Don't confuse this with the right hand rule for vector products, which is an arbitrary convention.)