FWLec12 - A. F. Peterson: Notes on Electromagnetic Fields...

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Unformatted text preview: A. F. Peterson: Notes on Electromagnetic Fields & Waves 10/04 Fields & Waves Note #12 Current, Conductivity, and Resistance Objectives : Introduce the concepts of electric current and current density. Discuss Ohm’s Law and the conductivity of materials. Illustrate the relation between the conductivity and resistance of a bulk conductor. Finally, present an expression for the power dissipation in conductive materials. In Note #5, the effect of an electric field on an insulated conductor was considered. In that environment, charges quickly redistribute themselves in order to cancel the electric field in the conductor. If on the other hand the conductor is not insulated, the charges are free to move. In this Note, we introduce the notion of a continuous movement of charge: a current . We also consider a means for characterizing different conducting materials in terms of their effect on the resulting current flow. The resistance associated with a uniform piece of conducting material is calculated. Finally, we present an expression for the power dissipation in a conducting material. Electric current Figure 1 depicts a battery with its terminals connected by a conducting wire. Chemical reactions within the battery maintain a voltage difference between the terminals, and therefore produce an electric field within the wire. Since the wire is a conductor, free electrons in the wire are subjected to a coulomb force F QE = applied (12.1) Consequently, these electrons will move in response to the applied force. An observer located at some point along the wire will observe a certain number of Coulombs of charge passing that point each second. Moving charge constitutes a current. The units of current, Amperes (A), satisfy 1 Ampere 1 Coulomb second = (12.2) Negative charge (electrons) moving in one direction is equivalent to positive charge moving in the other. Since the wire and the battery in Figure 1 comprise a closed loop, current will continue to flow as long as the battery is connected to the wire (until the original energy stored in the battery is exhausted). Current and current density Like charge, current comes in several flavors depending on the situation. The total current flowing past a particular point in a system is measured in Amperes. Current can also be distributed across a surface, or throughout a volume. In those situations, we can consider A. F. Peterson: Notes on Electromagnetic Fields & Waves 10/04 the current density at a particular point on the surface of a conductor or within a conductor volume. The different distributions of current can be summarized as follows: Total current I (A) Surface current density J s (A/m) Volume current density J (A/m 2 ) Although these are written as scalars, the electric current is usually expressed as a vector quantity, with the vector indicating the direction of current flow.quantity, with the vector indicating the direction of current flow....
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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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FWLec12 - A. F. Peterson: Notes on Electromagnetic Fields...

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