Lec2 - Winter 2008 Lecture 2 Electric Forces and Fields due...

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Lecture 2 Page 1 of 5 Lecture 2 Electric Forces and Fields due to linear charge distributions In the previous lecture, Coulomb’s law was introduced. This relationship indicated that charges will exert either an attractive (for unlike charges) or repulsive (for like charges) force on each other. In addition, electric fields were defined as the force per unit charge exerted at a point due to the presence of charges. These relationships were obtained for point charges. Point charges have no volume and consequently act as “elemental” sources. Most practical devices will have some physical dimension and consequently be more complicated than the simple point charge. These complex structures will often have continuous distributions of charge and as a result will require a more rigorous analytical process. In order to model the behavior of these complex structures, the concept of superposition and the linearity of electric fields (and forces) will be used. Line Charges : One of the basic structures used in electrical engineering is the wire. A wire is a linear piece of metal. Charges will accumulate on the wire and the resulting distribution of charge will produce an electric field. To model a line charge we need to define the distribution (or density function) of the charge on the line. The notation is typically ( 29 m C L r for line charge density. This may be a constant or a function of position along the line. In order to compute the field produced by a line charge we go to the definition of the electric field produced by multiple charges from lecture 1: = = N k k k k R R Q E 1 3 4 1 pe . In this case we can replace the point charge with a piece of the line charge (the piece will have a length of dl ). This leads to dl Q L k r = . Since the charge is a continuous distribution, it will be more effective to integrate the contributions (summing up each contribution for a continuous function is the job of an integral). This allows us to write the electric field as
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This note was uploaded on 04/17/2008 for the course ECSE 351 taught by Professor Davis during the Winter '08 term at McGill.

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Lec2 - Winter 2008 Lecture 2 Electric Forces and Fields due...

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