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homework7

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

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EE 151 Caltech Electromagnetic Engineering Spring ‘05 Homework 7 Due Thursday, May 26 th in class 1. ( Retarded Vector Potential ) Problem from Engineering Electromagnetics by Hayt and Buck. In a region where µ R = ε R = 1 and σ = 0, the retarded potentials are given by V = x ( z-ct ) V and A = x ( z/c-t ) a z Wb/m, where c = 1/sqrt( µ 0 ε 0 ). (a). Show that t V = µε A (b). Find B , H , E and D . (c). Show that these results satisfy Maxwell’s equations if J and ρ v are zero. 2. ( Dipole Antenna ) Problem from Engineering Electromagnetics by Hayt and Buck. A dipole antenna in free space has a linear current distribution. If the length d is 0.02 λ , what value of I 0 is required to: (a). provide a radiation field amplitude of 100mV/m at a distance of 1mi, at θ = 90 0 ; (b). radiate a total power of 1 W? 3. ( Antenna ) A square loop antenna, in which a time-harmonic current Ie j ω t is circling, is located in the x-z plane as shown in Figure below. Consider a point P (0,0,z) in the far field of the loop antenna.

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