Formal Definitions of Electromotive Force
Inside a source of emf that is open-circuited, the conservative electrostatic field created by separation of charge exactly cancels the forces producing the emf. Thus, the emf has the same value but opposite sign as the integral of the electric field aligned with an internal path between two terminals A and B of a source of emf in open-circuit condition (the path is taken from the negative terminal to the positive terminal to yield a positive emf, indicating work done on the electrons moving in the circuit). Mathematically:
where Ecs is the conservative electrostatic field created by the charge separation associated with the emf, dโ is an element of the path from terminal A to terminal B, and โยทโ denotes the vector dot product. This equation applies only to locations A and B that are terminals, and does not apply to paths between points A and B with portions outside the source of emf. This equation involves the electrostatic electric field due to charge separation Ecs and does not involve (for example) any non-conservative component of electric field due to Faraday's law of induction.
In the case of a closed path in the presence of a varying magnetic field, the integral of the electric field around a closed loop may be nonzero; one common application of the concept of emf, known as "induced emf" is the voltage induced in a such a loop. The "induced emf" around a stationary closed path C is:
where now E is the entire electric field, conservative and non-conservative, and the integral is around an arbitrary but stationary closed curve C through which there is a varying magnetic field. Note that the electrostatic field does not contribute to the net emf around a circuit because the electrostatic portion of the electric field is conservative (that is, the work done against the field around a closed path is zero).
This definition can be extended to arbitrary sources of emf and moving paths C:
which is a conceptual equation mainly, because the determination of the "effective forces" is difficult.
Read more about this topic: Electromotive Force
Famous quotes containing the words formal, definitions and/or force:
“That anger can be expressed through words and non-destructive activities; that promises are intended to be kept; that cleanliness and good eating habits are aspects of self-esteem; that compassion is an attribute to be prized—all these lessons are ones children can learn far more readily through the living example of their parents than they ever can through formal instruction.”
—Fred Rogers (20th century)
“What I do not like about our definitions of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.”
—G.C. (Georg Christoph)
“If you were to destroy the belief in immortality in mankind, not only love but every living force on which the continuation of all life in the world depended, would dry up at once.”
—Feodor Dostoyevsky (1821–1881)