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im kind of confused, the right hand rule is used to know where the direction the magnetic field created by the current is going .

is there any particular reason why the right hand is used to determine the direction of the Magnetic field?

jeo
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  • Duplicate: http://physics.stackexchange.com/questions/1229/is-there-any-situation-in-physics-where-the-right-hand-rule-is-not-arbitrary ? I'll merge them unless people think they should stay separate. – David Z Sep 16 '11 at 22:45

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No, there is nothing special about your right hand as compared to your left one. (Well, there might be, if you're a baseball player or a fiance, but there's nothing in classical electromagnetism that makes it special.)

If you set up two wires next to each other and run current through them, they will attract if the current runs the same way and repel if it runs opposite directions. As long as the way you're doing electromagnetism reproduces this and other experimental results accurately, your system of electromagnetism is valid.

If you use a left-hand rule, you'll essentially multiply all cross products by $-1$. That means the $B$-field calculated from a law like $\nabla \times B = J + \frac{\partial E}{\partial t}$ will be multiplied by $-1$. However, when you look at the Lorentz force law, which says $F = q(E + v\times B)$, there will be another $-1$ introduced by the second cross product, and the force on a charged particle comes out the same. Or if you look at the Poynting vector $E\times B$, that also gets another factor of $-1$ so energy flux comes out the same.

The reason to use the right-hand rule is that everyone else uses it, so when you see a picture with magnetic field lines drawn, the author has always used the right-hand rule to generate that picture.

Mark Eichenlaub
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  • ""No, there is nothing special about your right hand as compared to your left one. "" Nothing aside being chiral, meaning "handedness". Makers of gloves know that. – Georg Sep 16 '11 at 20:31
  • Of course left and right hands are kinematically different. That basic fact underlies the answer. The point is that despite the kinematic differences between left and right handed chirality, the physics is the same. There is no electromagnetic phenomenon that works with a right-handed version, but doesn't work with a left-handed version. – Mark Eichenlaub Sep 17 '11 at 02:37
  • ""hands are kinematically different"" O sancta simplicitas! – Georg Sep 17 '11 at 18:59
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It's convention. If Benjamin Franklin had used the opposite convention for positive and negative charges (electrons positive, protons negative), we'd probably be using the left hand rule in order to cancel out the sign change we'd get out of ${\vec F} = q {{\vec v} \times {\vec B}}$.

People will probably get into obnoxious pedantry involving hodge star and the fact that $\epsilon_{xyz}=1$, but all that was developed to describe electromagnetism, not the other way around. Had it been more convenient to start with, we would have defined a different cross product/Levi Civita symbol/hodge star that is different than ours by a minus sign, and we would be using the left hand rule.

Zo the Relativist
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  • In retrospect, I realize a simpler solution to fix Maxwell's equations in a $q$-reversed world would be to just reverse the direction of the magnetic and electric fields. Either way, it is still just convention. – Zo the Relativist Sep 16 '11 at 12:38
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The magnetic field was initially defined by the effect it had on a bar-magnet/compass: The direction was indicated by the north pole, and magnitude by the torque aligning the bar magnet with the magnetic field. It was then found that a wire carrying a current creates a magnetic field, with the direction of current being defined as the direction in which positive charge moves when a potential difference is placed across the wire. The direction of the magnetic field is then given by the right hand rule.

So the right hand rule was used because of the way the magnetic field and direction of conventional current was defined, and is still used today because more modern definitions are still compatible with the initial ones. Defining the direction of the magnetic field to be indicated by the south pole, or choosing the direction of negative charge flow instead of positive flow for the direction of current would mean we'd be using the left hand rule today, whereas changing both would leave us still with the right hand rule.

John McAndrew
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