Electromotive force on a Moving Conductor (64) Let a short straight conductor of length a parallel to the axis of x move with a velocity whose components are dx/dt dy/dt dz/dt and let its extremities slide along two parallel conductors with a velocity ds/dt Let us find the alteration of the electromagnetic momentum of the circuit of which this arrangement forms a part. In unit of time the moving conductor has travelled distances dx/dt dy/dt dz/dt long the directions of the three axes, and at the same time the lengths of the parallel conductors included in the circuit have each been increased by ds/dt Hence the quantity [integral](F dx/ds + G dy/ds + H dz/ds)ds will be increased by the following increments a(dF/dx dx/dt + dG/dy dy/dt + dF/dz dz/dt) due to motion of conductor a ds/dt(dF/dx dx/ds + dG/dx dy/ds + dH/dx dz/ds) due to lengthening of circuit The total increment will therefore be a(dF/dy  dG/dx)dy/dt  a(dH/dx  dF/dz)dz/dt or by the equations of Magnetic Force (8) a([mu][gamma]dy/dt  [mu][beta]dz/dt) If P is the electromotive force in the moving conductor parallel to x referred to unit of length, then the actual electromotive force is Pa and since this is measured by the decrement of the electromagnetic momentum of the circuit, the electromotive force due to motion will be P = [mu][gamma]dy/dt  [mu][beta]dz/dt (36)
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Manuscript details
 Author
 James Clerk Maxwell
 Reference
 PT/72/7
 Series
 PT
 Date
 1864
 IIIF

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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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