Given the rather narrow text measure that's in effect, I can't help but feel but that this example would be suited ideally for use of the \shortintertext command provided by the mathtools package (a superset of the amsmath package).
\documentclass{scrartcl}
\KOMAoptions{fontsize = 10pt, headings = normal}
\usepackage{mathtools}
\usepackage{multicol}
\usepackage{siunitx}
\newcommand{\abs}[1]{\lvert#1\rvert}
\begin{document}
\begin{multicols*}{2}
\section*{Electric Charge}
\textsf{Coulomb's Law} describes the electrostatic force between
point electric charges $q_1$ and $q_2$ at (or nearly at) rest and
separated by distance~$r$:
\begin{align}
F_c &= \frac{1}{4\pi\epsilon_0}\frac{\abs{q_1}\abs{q_2}}{r^2}
= \frac{k\abs{q_1}\abs{q_2}}{r^2}\\
\shortintertext{where}
e_0 &= \SI{8.85e-12}{\coulomb\squared\per\newton\per\meter\squared}\\
\shortintertext{and}
k &= \SI{8.99e9}{\newton\meter\squared\per\coulomb\squared}\,.
\end{align}
\end{multicols*}
\end{document}
With amsmath there is the aligned environment you can use inside other building blocks; it inserts a tiny space before it which may be undone with \!.
If you use the combination of split inside equation instead one align, then only one equation number is attached and you avoid writing \notag many times. By default the number is centered, but the tbtags option will place it on the final line.
If you load mathtools, which loads amsmath, you can shove the first line left easily with \MoveEqLeft, rather than having to find specify a unusual alignment point in that line. The command takes an optional argument, a number specifying how many ems to move left, the default is 2.
I illustrate two different ways of including an aligned block, they give different vertical spacing to the equation number.
\documentclass{article}
\usepackage[tbtags]{mathtools}
\begin{document}
\begin{equation}
\begin{split}
\MoveEqLeft
P(\mathcal{X},\mathcal{C},\xi|\alpha,\beta,\theta^0) \\
&= \prod_d P(\mathcal{X}_d|\beta)P(\mathcal{C}_d|\alpha,\xi)
\prod_c P(\xi^c|\theta^0) \\
&\propto\prod_d \beta^d_c\!\begin{aligned}[t]
&\left(F(\mathcal{C}_d)\prod_t
(\mathcal{C}_{dt})^{\alpha\xi_t}\right)\\
& \left( \prod_c F(\xi^c)\prod_t(\xi_t)^{\theta^0_t} \right)
\end{aligned}\\
\end{split}
\end{equation}
or
\begin{equation}
\begin{split}
\MoveEqLeft
P(\mathcal{X},\mathcal{C},\xi|\alpha,\beta,\theta^0) \\
&= \prod_d P(\mathcal{X}_d|\beta)P(\mathcal{C}_d|\alpha,\xi)
\prod_c P(\xi^c|\theta^0) \\
&\,\begin{aligned}[b]\propto\prod_d \beta^d_c
&\left(F(\mathcal{C}_d)\prod_t
(\mathcal{C}_{dt})^{\alpha\xi_t}\right)\\
& \left( \prod_c F(\xi^c)\prod_t(\xi_t)^{\theta^0_t} \right)
\end{aligned}
\end{split}
\end{equation}
\end{document}
Best Answer
Single line equations should never be in
align(even without the\textrequirement).You could use
Although probably I'd look at using an environment defined with
\newthoremrather than math mode for this.