  Let $\mathcal{K}^{r_0}_{x_0}$ be a (non-degenerate) truncated corner in
$\mathbb{R}^3$ with $x_0\in\mathbb{R}^3$ being its apex, and $\mathbf{F}_j\in
C^\alpha(\overline{\mathcal{K}^{r_0}_{x_0}}; \mathbb{C}^3)$, $j=1,2$, where
$\alpha$ is the positive H\"older index. Consider the following electromagnetic
problem $$\left\{\begin{split} & \nabla\wedge \mathbf{E}-\mathrm{i}\omega \mu_0
\mathbf{H}=\mathbf{F}_{1} \quad \mbox{in $\mathcal{K}^{r_0}_{x_0}$},\\ & \,
\nabla\wedge \mathbf{H}+\mathrm{i}\omega\varepsilon_0 \mathbf{E}=\mathbf{F}_{2}
\quad \mbox{in $\mathcal{K}^{r_0}_{x_0}$}, \\ &\, \nu\wedge
\mathbf{E}=\nu\wedge\mathbf{H}=0 \qquad\mbox{on $\partial
\mathcal{K}^{r_0}_{x_0}\setminus \partial B_{r_0}(x_0)$}, \end{split}\right.$$
where $\nu$ denotes the exterior unit normal vector of $\partial
\mathcal{K}^{r_0}_{x_0}$. We prove that $\mathbf{F}_1$ and $\mathbf{F}_2$ must
vanish at the apex $x_0$. There are a series of interesting consequences of
this vanishing property in several separate but intriguingly connected topics
in electromagnetism. First, we can geometrically characterize non-radiating
sources in time-harmonic electromagnetic scattering. Secondly, we consider the
inverse source scattering problem for time-harmonic electromagnetic waves and
establish the uniqueness result in determining the polyhedral support of a
source by a single far-field measurement. Thirdly, we derive a property of the
geometric structure of electromagnetic interior transmission eigenfunctions
near corners. Finally, we also discuss its implication to invisibility
cloaking.
