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EE 151 Caltech Electromagnetic Engineering Spring ‘05 Homework 7 Due Thursday, May 26thin class 1. (Retarded Vector Potential) Problem from Engineering Electromagnetics by Hayt and Buck. In a region where µR= εR = 1 and σ= 0, the retarded potentials are given by V = x(z-ct) V and A= x(z/c-t)azWb/m, where c= 1/sqrt(µ0ε0). (a). Show that tV∂∂−=⋅∇µεA(b). Find B, H, Eand D. (c). Show that these results satisfy Maxwell’s equations if Jand ρvare zero. 2. (DipoleAntenna) Problem from Engineering Electromagnetics by Hayt and Buck. A dipole antenna in free space has a linear current distribution. If the length d is 0.02λ, what value of I0is required to: (a). provide a radiation field amplitude of 100mV/m at a distance of 1mi, at θ= 900; (b). radiate a total power of 1 W? 3. (Antenna) A square loop antenna, in which a time-harmonic current Iejωtis 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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