| course |
course_year |
question_number |
tags |
title |
year |
Electromagnetism |
IB |
14 |
|
Paper 4, Section I, $5 \mathrm{D}$ |
2021 |
Write down Maxwell's equations in a vacuum. Show that they admit wave solutions with
$$\mathbf{B}(\mathbf{x}, t)=\operatorname{Re}\left[\mathbf{B}_{0} e^{i(\mathbf{k} \cdot \mathbf{x}-\omega t)}\right]$$
where $\mathbf{B}_{0}, \mathbf{k}$ and $\omega$ must obey certain conditions that you should determine. Find the corresponding electric field $\mathbf{E}(\mathbf{x}, t)$.
A light wave, travelling in the $x$-direction and linearly polarised so that the magnetic field points in the $z$-direction, is incident upon a conductor that occupies the half-space $x>0$. The electric and magnetic fields obey the boundary conditions $\mathbf{E} \times \mathbf{n}=\mathbf{0}$ and $\mathbf{B} \cdot \mathbf{n}=0$ on the surface of the conductor, where $\mathbf{n}$ is the unit normal vector. Determine the contributions to the magnetic field from the incident and reflected waves in the region $x \leqslant 0$. Compute the magnetic field tangential to the surface of the conductor.