Electromotive Force and Change of Flux

Author: E.E. Kimberly

If the conductor of Fig. 1-4 were entirely above the magnetic field and its ends were connected by a loop of wire hanging below the field, the field would be entirely enclosed by the link or turn of conductor so formed. If then the link were dropped downward an inch, it would no longer encircle or link any flux. The flux in the conductor link would then have changed in the amount of ϕ, the flux of the field. The flux lines of the field itself are closed links, as shown in Fig. 1-2. Therefore, the linkages of the flux lines with the conductor link would have been changed; in this case, they would have been reduced to zero.

The voltage generated in the conductor link would be proportional to the rate of change of total flux linkages. If the downward movement were accomplished in 1 second and the links of flux were 10⁸ lines, the average voltage generated would be 1 volt because the flux linkage change per second would be 10⁸1 = 10⁸. The equation of the voltage at any instant in the movement of the conductor link is then

[1-1]

This equation is the same as equation 1-1, but N is the number of conductor links or turns (1 in this case). The flux-linkage viewpoint then leads to the same result as the conductor-cutting-flux viewpoint. The flux-linkage theory will be enlarged under the subject of inductance in a subsequent chapter.

If - instead of being moved as described - the conductor had been held fixed while the flux was reduced to zero in 1 second, the rate of change of flux linkages and hence the average voltage generated would have been the same. That is the principle of the power distribution transformer.