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

The problems of this section use the wave equation of a simple medium, its one-dimensional solution and the potentials,

\nabla^{2} u - \frac{1}{v ^{2}} \frac{\partial ^{2} u}{\partial t ^{2}} = 0, v = \frac{1}{μ ε} = \frac{c}{μ _{r} ε _{r}}, u = f (z - v t) + g (z + v t), \nabla^{2} E - μ ε \frac{\partial ^{2} E}{\partial t ^{2}} - μ σ \frac{\partial E}{\partial t} = 0, B = \nabla \times A, E = - \nabla V - \frac{\partial A}{\partial t}, \nabla \cdot A + μ ε \frac{\partial V}{\partial t} = 0, A = \frac{μ}{4 π} \int_{V^{'}} \frac{J ( r ^{'} , t - R / v )}{R} d v^{'}, V = \frac{1}{4 π ε} \int_{V^{'}} \frac{ρ _{v} ( r ^{'} , t - R / v )}{R} d v^{'},

where $u$ is any Cartesian component of $E$ or $H$ . The constants are those of this course, $ε_{0} = 1 0^{- 9} / (36 π) = 8.842 \times 1 0^{- 12} F/m$ , $μ_{0} = 4 π \times 1 0^{- 7} H/m$ , hence $c = 1/ μ_{0} ε_{0} = 3 \times 1 0^{8} m/s$ and $η_{0} = μ_{0} / ε_{0} = 120 π Ω$ .

5.5.12 Problems and solutions

In this part

Problems · 6

Home exercises · 4

Further exercises · 10

Worked examples · 3