A straight wire of length l is moved at right angles (with a velocity v) across a magnetic field of strength B. The wire will have an induced current I flowing through it and will thus experience a motor force on it given by F = B × I × L
Lenz’ Law states that the motor force will oppose the movement of the wire (i.e. the force will be in the opposite direction to the wire’s movement).
The rate at which mechanical work is being done (i.e. power) against the motor force is given by P = F × v = B × I × L × v
We have previously derived an expression for the e.m.f. induced across such a straight wire: F = B × L × v
The electrical power generated in the wire is then the product of the e.m.f. and the induced current : P = B × I × L × v = E × I