Electromagnetic Fields and Waves: Notes, Solved Problems and Interactive Lab

About the further exercises of Section 6.2

Thirteen further exercises in the spirit of the problems, the worked examples and the home exercises, graded from easy to harder within each group. Exercises 6.2.1–6.2.3 are about lossy media and the loss tangent, Exercises 6.2.4–6.2.5 about good conductors and the skin effect, Exercises 6.2.6–6.2.8 about plasmas and the group velocity, and Exercises 6.2.9–6.2.13 come from the exercise lecture and mix all three. They use only the equations listed at the head of this subsection, together with $v_{g} = d ω / d β$ and $γ η_{c} = j ω μ$ , $γ / η_{c} = σ + j ω ε$ .

Exercise 6.2.2

Why ice defrosts slowly

At $2.45 GHz$ ice (about $- 10^{\circ} C$ ) has $ε_{r} = 3.2 - j 0.003$ , liquid water $ε_{r} = 78 - j 10$ (Worked example 6.2.1, $α_{w} = 29.0 Np/m$ ). (a) Find the loss tangent and the effective conductivity of ice and classify it. (b) Find $β$ , $λ$ and, with the low-loss formula, $α$ and the power penetration depth $D_{p} = 1/2 α$ of ice. (c) What fraction of the power entering a $5 cm$ thick block is absorbed in one pass, for ice and for water (reflections neglected)? (d) Find $η_{c}$ of ice.

Try it yourself first.

cf. Worked example 6.2.1

Exercise 6.2.2: Why ice defrosts slowly