Question

2. (a) Consider the propagation of a plane electromagnetic wave in a conductor. Show that the wavenumber, k, as a function of a, is given by the dispersion relationship ex ωε ωε where σ is the conductivity, μ is the permeability and ε is the permittivity of the conducting medium. (Hint: start with Maxwell's equations, and develop an equation of the form, V" E -k 2 E ). (3 marks) (b) Write down an expression for the physical electrical field inside a poor conductor distinguishing carefully between phase and amplitude terms. Sketch the instantaneous form of the field with propagation distance (3 marks) (c) In the case of a good conductor, derive the expression for the skin depth μσω (2 marks) Calculate the ocean depths at which a 1 μν/m E-field will be obtained for an E-field at the surface of 1 V/m for the following frequencies (a) 10 kHz, (b) 10 MHz. Assume (d) (2 marks)

Answer 1

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