J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’

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                                (65) The complete equations of Electromotive force on a moving 
conductor may now be written as follows 

Equations of Electromotive Force 

P = [mu]([gamma] dy/dt - [beta] dz/dt) - dF/dt - d[psi]/dx 
Q = [mu]([alpha] dz/dt - [gamma] dx/dt) - dG/dt - d[psi]/dy 
R [=] [mu]([beta] dx/dt - alpha] dy/dt) - dH/dt - d[phi]/dz (D) 

The first term on the right hand side of each equation 
represents the electromotive force arising from the motion of 
the conductor itself. This electromotive force is perpendicular 
to the direction of motion and to the lines of magnetic force 
and if a parallelogram be drawn whose sides represent 
in direction and magnitude the velocity of the conductor 
and the magnetic induction at that point of the field 
then the area of the parallelogram will represent the 
electromotive force due to the motion of the conductor. 
The second term in each equation indicates the effect 
of changes in the position or strength of magnets or 
currents in the field. 

The third term shows the effect of the electric potential [psi] 
It has no effect in causing a circulating current in a 
closed circuit. It indicates the existence of a force urging 
the electricity to or from certain definite points in the field
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Manuscript details

James Clerk Maxwell
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Cite as

J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7



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