“Magnetic mnemonics”

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?

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Standard model is a chiral theory. Surely that solves all the problems! :-) – Marek Jan 11 '11 at 12:10
Haha, I like that picture! Indeed all these "hand rules" can be pretty damn confusing sometimes. I prefer just to memorise the formulae, and the definition of the cross product. – Noldorin Jan 12 '11 at 14:36

7 Answers

Dear Kostya, 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.

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With all due respect @Lubos while your political pun is indeed pretty funny, it is probably best if we check our political beliefs at the door when using this site. The debates here are spicy enough as it is. Adding ideology to this mix might make it explosive and could also be seen as a disservice to the physics aspect of this enterprise ... IMHO. – user346 Jan 14 '11 at 7:43

To get the right answer, you should use the right hand, which happends to be the right hand, it cannot possibly get simpler

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Imagine yourself forgetting the right answer. Do you honestly believe that your reasoning will be convincing? Note that there are "left hand rules that are right" for electrodynamics as well. – Kostya Jan 11 '11 at 14:16
@Kostya So you are imagining forgetting this rule, but remembering some other more complicated mnemonic? Then I cant help you. You have to remember something in the end. – TROLLKILLER Jan 11 '11 at 14:23
I remember using left hand and got right answer. I see it starts to be subjective. But anyway your "answer" is not an answer, you can't expect that everyone have read the discussion. – Kostya Jan 11 '11 at 14:50
Mathematically, the left hand does not exist. Period. ;-) – Greg Graviton Jan 12 '11 at 12:36
Sure it does, in a left-handed co-ordinate system! They're just not very conventional. – Noldorin Jan 12 '11 at 14:37

Three points I'll like to address:

1) Use cross product as much as possible. If I give you a and b make sure you know which direction a cross b is pointing in. This is essential for many things beyond EM. Then you can state a law of physics without referring to your left or right hand: for instance the magnetic force on a moving particle is q (v cross B).

Of course to define cross product you might have to use your hand... try to find a definition that involves your right hand (the reason is given later).

2) To find the B field induced by a current point the thumb of your right hand towards the direction of the current. The fingers of your right hand are now curling in a certain direction (counterclockwise if the current is flowing into your face); this is the B field. This is non-negotiable; I'm sorry, the B field is defined such that this is true. And I am pretty certain there is no way of using your left hand to calculate this easily.

3) To find E field induced by changing B field, read up on Lenz's law. If you're OK with the previous two this should be trivial.

Now you should see why I recommended you use right hand to define cross product; you must use your right hand in step 2, so might as well use it in step 1 too.

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Thank you for the answer, but the requirement that I use my right hand is exactly my problem. I used this very mnemonic once -- then after a year I forgot: "was it left or right hand". – Kostya Jan 11 '11 at 13:27
Using right hand for (2) is non-negotiable; left hand will give the wrong answer. You can't really do (2) without referring to a hand. – xuanji Jan 11 '11 at 13:37
Come on. I need a mnemonic to remember the right answer. That's exactly why one needs a mnemonic. Of course the left hand will give the wrong answer -- that is the problem. To remember the right answer I have to remember which hand to use, while to remember which hand to use I have to remember the right answer. – Kostya Jan 11 '11 at 13:42
Sorry, I know remembering to use the right hand rather than left is pretty arbitrary. I don't know any way around the arbitrariness. Well, one thing that may have helped me is that I have never in my life used my left hand, everything was either cross product or right-hand rule. So I won't ask "left or right" because I've never used left. – xuanji Jan 11 '11 at 13:54
Do you not see what you are writing? To get the right answer use the right hand! The right hand to use is the right hand ! – TROLLKILLER Jan 11 '11 at 14:04

I actually encounter the same problem all the time, but I just save myself by using my right hand. The mnemonic I have been taught for 2 is very, very simple. Just imagine grabbing a wire with your hand so that your thumb is along the direction of current. Now your fingers are curled around it and that's the direction of the magnetic field!

So, if you need to find the direction of current just see the direction of the field and imagine wrapping something with it using your fingers. The direction your thumb points in is the direction of the current.

Oh and can you remember the cases in which the left hand applies? If you do then just use the above rule with your left hand...

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I'm just making these up as I go because we "always" use the right hand in the sense that our coordinate system (xyz) is always defined by the right hand rule, but:

For the cross-product, such as E = q(v cross B): ROD - right, out, down. If the first quantity (v) points to the right and the second (B) points out of the page, i.e. toward you, then the third (E) points down. I realize that "out" as out of the page may cause some problem, so you could substitute "at," meaning the vector points at you, and use RAD instead. I'd stick with ROD, though, so you don't think the A means "away" a year from now.

For magnetic fields in wires: RAA (think of the music industry). If the current flows to the Right, the magnetic field Above the wire points Away from you. Since you know the magnetic field is a circle around the wire, this establishes the field direction.

This is all for positive charge/current, since that's the physics standard. In both these cases, use the mnemonic to establish the right hand rule and go from there, since that's probably easier than trying the rotate your problem to match the mnemonic.

As one last note, if ROD (right, out, down) and RAA (right, above, away) slip, if you have a coordinate system drawn, x cross y = z will force you to remember it's your right hand to use.

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As with all mnemonics, you just have to try lots until you find one that resonates with you ... Here's mine, I don't know if it will help.

There are 2 "hand" rules for electromagnetism: the left-hand motor rule, and the right-hand current rule.

Left-hand motor rule

The left-hand motor rule shows what happens when a current-carrying wire moves in a magnetic field. Hold the thumb, first and second fingers mutually perpendicular. Then:

• The thuMb gives Movement (or equivalently the THumb gives THrust)
• The First finger is the direction of the magnetic Field
• The seCond finger is the direction of the Current

Together these give you the direction of force on a wire when current flows through it in a magnetic field (motor), or the direction of current induced in a wire when the wire moves in a magnetic field (inductor).

Right-hand rule - direction of magnetic field around a wire

Grab the wire with your right hand; the thumb points in the direction of the current, and the fingers curl around in the direction of the magnetic field.

Left or right hand?

Well, I'm left-handed. So I associate the motor rule with my left hand - I do most stuff with my left, which is controlled by my motor neurones. Then the other rule uses the other hand. I accept that may not help if you're right-handed :-)

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I see you don't like the other answers. I don't think anyone can help you and here's why.

In EM there is no way to get around arbitrariness of defining orientation (because the theory is P, as well as C and T symmetric). So you just have to remember the whole set orientation + hand trick. I assume you learned both your first name and the last name and there the arbitrariness is substantially larger than just choosing left or right. So just pick one and stick it into your brain. I hope you can learn a bit (pun intended).

That being said, there might be a loop-hole. You can pick non-chiral theory (weak interactions) which tells you which orientation is "correct" (similarly like matter is more "correct" than antimatter in our universe). Quoting wikipedia on parity violation: "The Standard Model incorporates parity violation by expressing the weak interaction as a chiral gauge interaction. Only the left-handed components of particles and right-handed components of antiparticles participate in weak interactions in the Standard Model." This is a useful piece of information of and by itself, so I hope you don't mind learning it.

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Thanks Marek. It is true that problems are due to the discrete symmetry. And I understand that at least something have to be remembered. – Kostya Jan 12 '11 at 9:52
It is possible to add a link for that wikipedia quote? thx – Steven Devijver Jan 12 '11 at 12:13
I shudder to think what it would be like trying to teach intro-level physics students about parity violation! :-P – David Z Jan 13 '11 at 7:28
@David details are surely non-trivial but every high school kid knows about matter/antimatter asymmetry nowadays, right? So qualitative picture can be given pretty easily. – Marek Jan 13 '11 at 9:09
@Marek: well, I'm not sure. Of course they know that there is more matter than antimatter around us but I wouldn't be surprised if some or most of them have never thought about it in detail before. I'm almost tempted to do a little survey in the class I'm teaching tomorrow ;-) Anyway, explaining the connection between matter-antimatter asymmetry and the choice of the right-hand rule vs. the left-hand rule would be the hard part. – David Z Jan 13 '11 at 9:20