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If a conducting rod moves through a magnetic field which way do its electrons move?

In my revision guide it shows the following picture (more or less, but the following is my drawing of it -- I didn't change anything):

enter image description here

I'm having trouble understanding why the electrons accumulate on the end of the rod shown in the picture. Surely by Fleming's left hand rule the flow of positive charge will be in the direction of the green arrow here:

enter image description here

Which means that the electrons flow in the opposite direction to the green arrow, so the "plus" and "minus" signs in the rod are the wrong way round in this diagram. It should be like:

enter image description here

Or am I doing something wrong?

Thanks!

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  • $\begingroup$ Fleming's left hand rule: index finger - field, middle finger - current. $\endgroup$ – AV23 May 5 '15 at 17:05
  • $\begingroup$ @AV23: Thumb -- thrust (force) $\endgroup$ – user45220 May 5 '15 at 17:06
  • $\begingroup$ Yes, that too. But I suspect the mistake is in associating quantities to these fingers. $\endgroup$ – AV23 May 5 '15 at 17:07
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    $\begingroup$ @AV23: No I did it like you said: field -- index finger, current -- middle finger, force -- thumb. But I think I know what I did wrong now, apparently I was meant to use my right hand instead because the current is being generated by motion, not the other way round. physics.stackexchange.com/questions/181260/… $\endgroup$ – user45220 May 5 '15 at 17:10
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    $\begingroup$ Well, the left hand rule is applicable here too, if you use it the right way - the "current" is due to the "Motion", and the force is where the charges are pushed to on the rod. (All following from $\vec{F} = q\vec{v}\times\vec{B}$) $\endgroup$ – AV23 May 5 '15 at 17:25
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Let us imagine that the charge carriers in the rod are electrons (negatively charged). An electron moving to the right is equivalent to a (conventional) current to the left. Alternatively, you can use a "left hand rule" for electrons (since the current is to the left when the motion is to the right, you can represent electron motion with the thumb of your left hand, or conventional current with the right hand).

Either way - with your right hand thumb pointing to the left, and your index finger pointing down, your middle finger is pointing towards you: so that is where the force of the magnetic field is pushing the electrons, and that is why the negative charge accumulates on the side of the rod facing you.

Your mistake was in looking at the divided charges and concluding there will be a current along the wire; as long as the rod is moving at a steady rate through a homogeneous magnetic field, there will be no flow along the rod (after the charge has split as shown).

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To use rules without knowing what is the reason is boring. See my paper about vector product for Lorentz force, for generators and for electric drives, in a reduced form for perpendicular vectors only. If one isn't sure that this equations could be derived see this answer from mathematicans. See my answer Why does one call $B$ the magnetic induction? too.

If one not want to make some the calculations but want to find the directions only you can use these vector products for every angle between these vectors expect zero angles. You have to use for all three equations or the right hand or the left hand (for the flow of electrons or for the technical direction of current).

Accepting these three equations one can see how electrons electric charge and electrons magnetic dipole moment and the movement of the electron are related.

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