Fundamentals of Electromagnetic Fields
Including numerous examples with complete, worked-out solutions, this book is designed to present the fundamental concepts of electromagnetic field theory as they relate to modern engineering applications.
TABLE OF CONTENTS Fundamentals of Electromagnetic Fields
Chapter 7: Maxwell s Equations for Time-Varying Fields
7.1 INTRODUCTION
The Maxwell equations for a static electric field and steady state magnetic field, which are time-independent field s are as follows:
| Point/Differential form | Integral form | |
|---|---|---|
| ? H=J | | (7 1) |
| ? E=0 | | (7 2) |
| ? ? D= ? v | | (7.3) |
| V ? B=0 | | (7 4) |
| The associated relations are: D= ? E, B= ? H, and Ohm s law J= ? E. | (7 5) |
In this chapter, two new concepts are introduced:
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An electric field produced by a changing magnetic field.
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A magnetic field produced by a changing electric field.
The first concept resulted from the experimental research of M. Faraday and the second resulted from the theoretical efforts of James Clerk Maxwell.
7.2 FARADAY S LAW
In 1820, Oersted demonstrated that an electric current affected a compass needle. Faraday professed his belief that if a current could produce a magnetic field, then the magnetic field should be able to produce a current. Faraday worked on this problem for 10 years until he was finally successful in 1831. He wound two separate windings on iron toroid and placed a galvanometer in one circuit and a battery in the other. Upon closing the battery circuit, he noted a momentary deflection in the galvanometer. A similar deflection in the opposite direction occurred when the battery disconnected. This was the first experiment he made involving a changing magnetic field.
In terms of fields, we now say that a time-varying magnetic field produces electromotive force which may...
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