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Biot–Savart law: the origin of chirality?

by carrz
Tags: biot–savart, chirality, origin
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carrz
#1
Jul15-14, 07:20 AM
P: 53
As we know Biot-Savart law follows right-hand rule, like this:




...so the question is why right-hand rule, why not left?

I suppose it must have something to do with electron's magnetic dipole moment or "spin", as that's the only source of asymmetry I am aware of in this scenario. It follows then the orientation of the spin axis could be what defines this magnetic rotational direction, which would imply then the spin axis orientation is defined by the velocity vector. But still, the question remains, how or why could velocity vector have any specific directional impact on either intrinsic electron spin axis orientation or Biot-Savart magnetic field rotation?
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Jano L.
#2
Jul16-14, 03:28 PM
PF Gold
P: 1,141
The right-hand rule works because it gives the same direction as the vector product in the Biot-Savart law:
$$
\mathbf j(\mathbf x') \times |\mathbf x - \mathbf x'|
$$
where ##\mathbf j## is current density at point ##\mathbf x'##, ##\mathbf x## is point where the magnetic field is sought.

The vector product chooses one direction for ##\mathbf B## from two possibilities. Direction of magnetic field could have been defined to be opposite. Then we would use left hand to get this opposite direction.
Matterwave
#3
Jul16-14, 08:13 PM
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P: 2,660
People use the right hand rule mostly because most people are right handed. It's easier to figure out the convention using the dominant hand. One can arbitrarily reverse all the fields and go by the left hand rule. The only physical effect is the motion of particles and forces on these particles inside these fields, so however direction you choose to define the fields is arbitrary as long as you get the motion correct in the end.

DaleSpam
#4
Jul19-14, 07:48 AM
Mentor
P: 16,947
Biot–Savart law: the origin of chirality?

Quote Quote by carrz View Post
...so the question is why right-hand rule, why not left?
This is merely a matter of convention. Like why the electron is negative, why not positive? EM could work just fine if we picked different conventions (i.e. electrons positive, left hand rule, different units, etc.) Someone historically picked the right hand and established the convention and people have just used it ever since, there is no physical reason nor effect.


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