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):



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*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.. 
 A: 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.
A: 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.
