Wed, 2015-01-14 11:29 — Sami Mohammad AL-Jaber

Research Title:

Generalization of Faraday’s Law of Induction: Some Examples
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Generalization of Faraday’s Law of Induction: Some Examples | 243.23 KB |

Research Abstract:

A
general form of the induced electromotive force due to time-varying magnetic
field is derived. It is shown that the integral form of Faraday’s law of
induction is more conveniently written in the covering space. The method used
in this work relies of finding the modified magnetic field each time the
circular path is traversed. This amounts to an additional time derivative of
the magnetic field. Therefore, the induced electromotive force comes from the
sum of all contributions coming from all winding numbers. Thus the differential
form is shown to relate the induced electric field in the n^{th} winding number to the (n+1)^{th }time- derivative of the magnetic field. It is
also shown that the higher order terms are modulated by the self-inductance and
resistance of the circuit. Some illustrative examples for time-dependent
magnetic fields are presented: Sinusoidal, exponential, and step-function
fields. In each of these examples, it is shown that the induced electromotive
force could be written in closed analytical form that depends (among other
things) on the ratio between the self-inductance and resistance of the circuit.
Furthermore, in all these examples it is demonstrated that our result for the
induced electromotive reduces to the well-known result in the limit of the
ratio of the self-inductance and resistance goes to zero. The conclusion of
this work shows that Maxwell’s equation of Faraday’s law of induction can be
written in a more general form in the physical space.