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    If an electron is moving due east, then when using the left hand rule, the second finger is pointing due west. If a positively charged particle is moving due east, do we still point our second finger due west.
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    What's 'the second finger'? The index finger i.e. the B-field?

    Also, remember the LHR applies to a positively charged particle. If it's negatively charged, all you have to do is flip your thumb (resultant force) 180 degrees (as F = qE is negative for negative q, and F is a vector)
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    The middle finger of your left hand always points in the direction of the flow of conventional current. By an accident of history, conventional current is the direction of flow of positive charge or current. If the charges are negative, the finger points in the opposite direction.
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    Stonebridge's point is correct. The 'second' finger always points in the direction of the flow of positive charge (its easier to imagine when your think of it in the 'current' sense) If electrons move one way; current moves the other. So if the question is concerning protons, the second finger goes in their direction; if its electrons, it goes in the opposite direction.
 
 
 
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