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Work done by the Lorentz force?

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When a wire is placed in a magnetic field and current flows in that wire work is done on the wire and be calculated:

1) W = Fd
2) F = IL x B
3) W = ( IL x B )x d

Must there be any derivations beyond what is above?
If everything is "given" or... measured via instruments.


Then when the wire starts to move, motional EMF can be calculated:
ε = -vBL

Is this correct?

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