How the fuck does the right-hand rule work

how the fuck does the right-hand rule work

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utm.edu/staff/cerkal/handrule.htm
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Being left-minded is more useful in an industrial and technological society so a right-hand rule is naturally and socially selected for. Maybe with UBI creative pursuits would see their value skyrocket, ushering in a left-hand rule.

If has nothing whatsoever to do with which side is "better". It's just an aid to remembering the relative directions of field, EMF, and motion. (Almost) everybody carries a right hand around with them at all times, which is convenient.

Easy-to-remember pictures at utm.edu/staff/cerkal/handrule.htm

but why does a magnetic field literally choose a side
it's like the universe is assymetrical
makes no sense

why does it not make sense for the universe to be assymetrical? where did the assumption that it should be symmetrical come from?

but how is a magnetized object propelled towards the left if it's near an electrical current flowing upwards?
I don't get it
am I even understanding this correctly?
also there's a third right hand rule that seems to have THREE different forces going in totally different directions
w t f

The answer is that it doesn't. The magnetic and electric field are made up things used for measurements, the more fundamental objects are the vector and scalar potential.

There, the magnetic field can be described as the curl of the vector potential, so you essentially use two right hand rules to calculate your final force, in which you would obtain the same answer if you used a left-handed coordinate system.

The magnetic field direction would point the other way in a left-handed coordinate system, but the force on a charge would be in the same direction for either.

Well, the magnetic field direction is given by Biot-Savart's law, which is an experimental discovery. There needs be a theorethical explanation I imagine, but at the moment I haven't done it that far in the college.

but if I have an electrical current flowing upwards
and a magnet at a certain distance from it
it literally says that the magnet will orbit around it in a counterclockwise direction
can someone explain
this is nonsense

I know that feel bro. I don't know what the fuck my lecturer is talking about, how can a field or object always move to the right hand side?

I dont fully understand. The force wont always be the same. It depends on the direction of B. If you have a charge moving upwards, and you have a perpendicular magnetic field, the direction of the force depends on the derection of the magnetic field. It can go to one way or the exact opposit. The magnetic field it's defined in a way for the right hand rule to work. I think (?

it's just a convention

fuckin magnets how do they work

magnets aren't real it's just moving charges interacting with each other

gazillion of electrons with their quantum spin aligned

R.h.r is just a easy way to remember cross products. If you worked in R^4 you'd have a hard time figuring it out.

it works because there are only two possible orientations of three cartesian coordinates around the origin, and those orientations are mirror images like your right and left hand
I don't know how to prove that though

The right hand rule is the result of convention. But the universe isn't symmetrical under reflection, you can read about it in this Feynman lecture (you might want to start at 52–5 if you're okay jumping in part way)

feynmanlectures.caltech.edu/I_52.html

Kinky

>I don't know how to prove that though
the space of all ordered basis of R^3 has two connected components: frames with a positive determinant and frames with a negative determinant

"connected components"? I'm also not sure I understand precisely how the sign flip of the determinant demonstrates orientation. forgive me, I haven't taken as much high level math as I'd like

He's saying you can use your left hand if you point your thumb down and then curl your hand. That would be analogous to flipping the middle row and another row of the coefficient matrix for the unit vectors.

Is everybody in this thread pretending to be retarded? The "right-hand rule" is only a thing because most of the defined coordinate systems are "right-handed", in that the right hand rule with x cross y gives you z. You can just as easily define a left-handed coordinate system that will give you the same results in physical phenomena if you are consistent.

yes, but: how do you know that all 3d cartesian coordinate systems are either right or left handed?
you can prove it geometrically by exhaustion but I feel like there should be a simpler way
how many orientations are possible for a 4d cartesian cordinate system? how do you figure it out?

the thing is using the fact that the sign of the determinant shows orientation seems like begging the question

For the 3 by 3 case, take the cross product. if positive x and y components produce a positive z component, it is a right handed system. You can extend this to an n by n case.

yes but how do you know that you can superimpose any two normal coordinate systems with the same-signed cross-product?

I don't really understand what you're asking.

in the 3x3 case, the cross product produces a third vector that is perpendicular to the two being crossed. In the case of the two basis vectors ('i' and 'j'), it produces another basis vector, 'k', all three of which are a basis for 3d space. you can extend this as before.

If you're asking why positive x positive = positive is chosen to be a "right-handed" coordinate system, that's probably just convention

say you have positive x, y, and z at right angles to each other. Either they obey the right hand rule or they obey the left hand rule. Any two sets that obey the same rule can be superimposed on each other through rotation. Any two sets that obey different rules cannot.
Why do these two rules cover the whole set? i.e. if you flip two axes why is the orientation the same as what you started with? and how does this work out in higher dimensions?

>Biot-Savart's law, which is an experimental discovery.

What the fuck?

Right hand and left hand rule is literally the same fucking thing. Left hand rule takes the flow direction of electrons into account, right hand the conventional direction of the electrical field which is opposed to the electron current.

>Any two sets that obey the same rule can be superimposed on each other through rotation

Right hand and left hand rule is literally the same fucking thing. Left hand rule takes the flow direction of electrons into account, right hand the conventional direction of the electrical field which is opposed to the electron current.

>Any two sets that obey the same rule can be superimposed on each other through rotation

Both rules are not rotated, they are mirrored just like your hands are you double nigger.

many laws were. e.g. the reason you have separate named laws for different relationships in the ideal gas law is because they were separate experimental discoveries. E&M went through a lot of torture to get to such a beautiful, simple result as Maxwell's equations

your left and right hands cannot be superimposed
similarly, right- and left- handed coordinate systems cannot be superimposed
but: if you flip the direction of TWO axes, you are back to where you started
this is pretty obvious if you play around with it for awhile but I don't know that there's a simple way to *derive* it. I think group theory? And I don't know what you can say about a higher-dimensional coordinate system's handedness

you can use left hand rule for both FBI and induced emf

it's just the way we do things. Why is north north, why do civilized countries drive on the right side of the road? It just works out that way if we do everything one way.