# FWLec5 - A. F. Peterson: Notes on Electromagnetic Fields...

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A. F. Peterson: Notes on Electromagnetic Fields & Waves 10/04 Fields & Waves Note #5 Conducting and Dielectric Materials Objectives : Discuss the basic methodology by which the electric field interacts with good conductors and dielectric materials. Introduce the relative permittivity and the electric flux density. Electromagnetic fields would be of little interest if they did not interact with materials in the environment. In this Note, the means by which the electric field interacts with two different types of materials is considered. For good conductors, the electric field has a substantial effect on the free electron distribution within the conductor. For dielectric materials, a similar effect leads to the phenomenon of dielectric polarization. For the purpose of discussion, we assume that the material effects are adequately modeled by atoms having a positively-charged nucleus surrounded by a cloud of negative charge (electrons). Conductors Conductors are materials, such as metals, that contain a large number of free electrons. Free electrons are able to move from one molecule to another within the material. As a consequence, conductors usually provide a good path for both heat and electricity. An applied electric field interacts with such a material primarily through its effect on the free electrons. Consider an insulated conductor in the presence of an applied electric field E applied . This field creates a force on the electrons within the material, according to Coulomb’s Law: FQ E = applied (5.1) Since the electrons have negative charge, they experience a force directed opposite that of E applied . The applied electric field also creates a force on the positively-charged nuclei in the direction of E applied . Consequently, if the conductor has no net electric charge to start with, there will be no net force on it due to an applied electric field. However, within the material, the nuclei are held in a fixed location, while the electrons are free to move. Therefore, there will tend to be a net movement of negative charge within the conductor in response to an applied field, as depicted in Figure 1. This negative charge will tend to bunch up on the surface of the conductor, since it cannot easily move outside the material, creating a surface charge density r s . As the negative charge moves to one side of the conductor, positive charge is left behind, creating an additional surface charge density on the opposite face of the material (Figure 1). The separation of positive and negative charges of equal value creates a configuration known as an electric dipole . These dipoles in turn excite an electric field of their own.

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A. F. Peterson: Notes on Electromagnetic Fields & Waves 10/04 Example: Charges of – Q and + Q are located at z = – d /2 and z = + d /2, respectively, on the z -axis (Figure 2). Find the E -field in the x - y plane due to this arrangement.

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## This note was uploaded on 01/27/2011 for the course ECE 3025 taught by Professor Citrin during the Spring '08 term at Georgia Institute of Technology.

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FWLec5 - A. F. Peterson: Notes on Electromagnetic Fields...

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