It Can Be Shown That . . .

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If the coil is wound such that the flux through each turn is the same (if the windings are parallel), the induced voltage is given by:

(1")     

where:

V is the induced voltage and

N is the number of turns.

Equation 1" can be rewritten as:

(2")     

where:

B is the strength of the magnetic field and

A is the area of the circuit exposed to the magnetic field.

From Equation 2" after substituting Lx for the area A:

(4)     

where:

Lx is the area of the coil that is exposed to the magnetic field,

x is the height of coils, and

dx/dt is the velocity of the coil movement.