Show all work. If you need to assume anything, state your assumptions clearly. Reasonable assumptions that are necessary to solve the problem will be accepted.
In all problems assume properties of free space (ε0 = 8.854x10-12 F/m, μ0 = 4Π x10-7 H/m, η0 =377 Ω, phase velocity in air: 3 x108 m/s
1. Two dipole antennas are given, both λ/2 in length, one operating at a frequency f1, the second operating at a frequency f2 >> f1. Both are made of copper, have a radius b and a conductivity a. Calculate the ratio of their efficiencies. Copper has permeability and permittivity of free space.