A 0.5-MHz antenna carried by an airplane flying over the ocean surface generates a wave that approaches the water surface in the form of a normally incident plane wave with an electric-field amplitude of 3,000 (V/m). Seawater is characterized by εr = 72, μr = 1, and σ = 4 (S/m). The plane is trying to communicate a message to a submarine submerged at a depth \( d \) below the water surface. If the submarine’s receiver requires a minimum signal amplitude of 0.01 (μV/m), what is the maximum depth \( d \) to which successful communication is still possible?

Given Data: Let us consider the given data, Conductivity σ=4 S/m Dielectric constant(εr)=72 Relative permeability μr=1 Frequency (f) = 0.5 MHz = 0.5×10-6 Hz To Find: The maximum depth dSolution: Sea water is a good conductor. For sea water at 0.5 MHz, α=ωμ∈21+σ2ω2∈2μ∈2=4π×10-7×1×72×8.85×10-122μ∈2=4×10-16σω∈=42π×0.5×106×72×8.85×10-12σω∈=1998.17σω∈2≃4×106α =2π ×0.5×1064×10-161+4×106-1α=2.8 Npm Given , E0=3000VmEdmin=0.01 μVmEdmin=E0e-αdmax0.01×10-6=3000 e-2.8dmaxdmax=ln30000.01×10-62.8dmax=9.438 mAnswer: Therefore,the maximum depth d =9.438m

Answered: A 0.5-MHz antenna carried by an…