Electromotive Force

When the flow of the Magnetic field which crosses a conducting circuit varies during time, it appears in this circuit a tension . The tension thus created is directed in order to generate currents being opposed to the variation flow. It is thus said that she is opposed to the variation flow. This tension is also called electromotive force .
The variation of the flow of the magnetic field can have two causes (nonexclusive):

Is the circuit is subjected to a fixed field but it is deformed or one obliges it to turn (case of the machines with D.C. current).
Is the circuit is motionless and the intensity of the magnetic field varies or turns (case of the alternator S).

f.e.m. (electromotive force) and f.c.e.m. (counter electromotive force)

The distinction between electromotive force and counter electromotive force is artificial: the physical phenomenon is single.

If the current, which circulates indeed in the driver, the fact according to the direction which enables him to be opposed to the flux variation then one says that one deals with f.e.m.: this f.e.m. is (sometimes partly) generating current which circulates.
If the current circulates in the other direction, one can name it counter electromotive force (but it is not an obligation) because it tends to be opposed to the flow of the current. This current in opposite direction cannot exist that if there exists another source of tension in the circuit which is opposed to the f.c.e.m. and which delivers a value of tension higher than the latter.

f.e.m. and Maxwell's equations

The existence of the f.e.m. rises from the one of the equations of Maxwell, the equation of Maxwell - Faraday

The local form of this equation is:
$\ vec {belch} \ vec E = - \ frac {\ partial \ vec B} {\ partial T}$

It becomes for a conducting contour C:
$E = \ oint_ {C} E DLL = - \ frac {D \ phi} {dt}$
where E represents the f.e.m.

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