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EE 151 Caltech Electromagnetic Engineering Spring ‘05 Homework 3 Due Tuesday, April 19thin 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) = V0sin(ωt) 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 wand lengthl. The insertion depth is b. Calculate the induced voltage Vindacross the loop. (b)Show that Where U(t) is the total electromagnetic energy stored inside the capacitor, Eand Hare, respectively, the electric and magnetic field vector. The integral is evaluated over the surface that encloses the volume between the two circular plates. b wal VincFigure 1
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