Why Are Fleming's Left and Right Hand Rules Opposite for Generators?

[gangsta316]

I think I know what Fleming's left hand rule but how does Fleming's right hand rule come about and why is it opposite for generators? Is Fleming's right hand rule just the left hand rule for electron flow (instead of current) or would it be more proper to use the left hand rule in that case but with current in the opposite direction to electron flow? Also, what about this right hand rule?
http://www.physics.ubc.ca/~outreach/phys420/p420_96/reg/rhr_lor.htm

 

[Bob S]

If you look at the standard Lorentz force with your right hand (F = I x B) in a mirror, you get Fleming's left hand rule.