# The direction of the Lorentz Force

We have a square loop (I believe it's called) in a uniform magnetic field between the 2 poles of a permanent magnetic field (green is N, red is S). P is connected to the positive pole of a voltage source and Q is connected to the negative pole (so there is a current):

• Show the direction of the Lorentz force

My idea:

The magnetic field lines point towards S from N. There is no Lorentz force at b, because the angle between the current and the field lines is $180^o$. Using the left hand rule we find that at h the lorentz force goes 'into' the paper and at the right side of h the Lorentz force goes out of the paper.

Problem:

My book says that the magnetic field lines face from N to S, which causes opposite answers. Why is this? I'm thinking it has to do something with $P$ and $Q$, but I'm not quite sure..

• I've often encountered that people on this site give good answers in the comment section. I would appreciate it if you won't do that here (unless it has a specific reason), so I can reward you for your answers. Jan 18, 2013 at 15:34
• Alright, roger that :-P Jan 18, 2013 at 15:39
• Is the green area on the left hand side the north magnetic pole? I can't make out the letter on the figure. Jan 18, 2013 at 15:41
• @b_jonas Yes, the green is the north magnetic pole. I'm sorry for the inconvenience, but I think I mentioned it in my question. Jan 18, 2013 at 15:43

The magnetic field direction you are considering when facing this exercise is opposite to your book's. The convention which appears in your book, of field lines coming out from the North pole and sinking into the South pole, is actually the standard convention that is used for the poles of a magnet.

It's all a matter of convention: One could choose to name the poles in the opposite way, and then the Lorentz torque would be in the direction you are describing... But I insist in that not being the usual convention.

• Wait, the convention is they point from N to S? I thought it was the other way around.. in every picture on google you see them pointing towards N when going into S? Jan 18, 2013 at 15:53
• This is actually a very funny story which has to do with History: The North pole of a magnet was called in such a way by European sailors and explorers because, well, basically it seemed to point to the geographical North pole. And if you think about it in the terms any layman would think before the development of the classical theory of electromagnetism (which took place in the 19th Century), you would have realised that the North pole of a magnet attracts // is attracted to the South pole of another magnet. Then the funny catch is: The Earth's 'North magnetic pole' is actually a South pole! Jan 18, 2013 at 16:02
• If you want me to do it, I can try to expand my answer and give a little more of historical insight in the whole convention :-) Jan 18, 2013 at 16:05
• Haha yes I did know that, I also found it funny, in the same way that current is actually opposite to moving electrons. I however was confused because I thought (and was taught) that magnetic field lines always point towards the north pole. Jan 18, 2013 at 16:11
• Another twist to the story: inside the magnet, the magnetic field lines have the opposite direction, from south to north. Quite similar to the current flowing from negative to positive inside a battery.
– jkej
Jan 18, 2013 at 17:12

You appear to be reversing two conventions. Those two reversals cancel out, giving you the correct final answer.

The first convention, as you note, is that magnetic field lines run from north to south.

You refer to a "left-hand rule." If I understand correctly how you are using that, the usual convention is a right-hand rule. Arrange your right hand so that your fingers point in the direction of the current. Curl your fingers towards the direction of the magnetic field; your thumb will point in the direction of the force.

You should notice a few things. Flipping the direction of the field will flip the direction of the force. Using your left hand instead of your right hand will flip the direction of the force. Doing both of those will cause those two flips to cancel out, returning you to the correct direction for the force.