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Electromechanical Dynamics (Part 1).0050

# Electromechanical Dynamics (Part 1).0050 - p hence J,= JX...

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Sq \ Surface S I/ enclosing SL / volume V - Equipotential bodies Fig. 2.1.6 A simple electric field system. Terminals are brought out so that excitation may be applied to the equi- potential bodies. It is conventional to select one equipotential body as a reference and designate its voltage as zero. The potentials of the other bodies are then specified with respect to the reference. As a simple example of finding the terminal relations for an electric field system, consider the two equipotential bodies in Fig. 2.1.6. We assume that the voltage v is impressed between the two equipotential bodies and wish to find the current i. We choose a surface S (see Fig. 2.1.6) which encloses only the upper equipotential body and apply the conservation of charge (1.1.26). The only current density on the surface S occurs where the wire cuts through it. At this surface there is
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Unformatted text preview: p,, hence J,= JX, so that J' -n da -i. (2.1.26) The minus sign results because the normal vector n is directed outward from the surface. The total charge q on the upper equipotential body in Fig. 2.1.6 is q = vp dV, (2.1.27) where V is a volume that includes the body and is enclosed by the surface S. Use of the conservation of charge (1.1.26) with (2.1.26) and (2.1.27) yields the terminal current dq S- dq (2.1.28) dt Equation 2.1.28 simply expresses the fact that a current i leads to an accumulation of charge on the body. For a quasi-static system in which we impose voltage constraints the field quantities and the charge density p, are determined by (1.1.24), (1.1.25) and (1.1.13), and all are functions of the 2.1.2 Circuit Theory A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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