homework3

# Engineering Electromagnetics with CD (McGraw-Hill Series in Electrical Engineering)

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EE 151 Caltech Electromagnetic Engineering Spring ‘05 Homework 3 Due Tuesday, April 19 th in class 1. An ideal parallel-plate capacitor is shown in Fig. 1 . The radius of each plate is a. The spacing between the two plates is h. A time-varying voltage V(t) = V 0 sin( ω t) is applied across the capacitor. Assume uniform field inside the capacitor and ignore fringing effects. (a) A rectangular-shaped open metal loop is inserted in the capacitor. The surface of the loop is parallel to the axis of the capacitor. The dimensions of the loop are width w and length l . The insertion depth is b . Calculate the induced voltage V ind across the loop. (b) Show that Where U (t) is the total electromagnetic energy stored inside the capacitor, E and H are, respectively, the electric and magnetic field vector. The integral is evaluated over the surface that encloses the volume between the two circular plates. b w a l V inc Figure 1

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