  In some extensions of the standard model of particle physics, the values of
the fundamental coupling constants vary in space and time. Some observations of
quasars hint at time and spatial variation of the fine structure constant
$\alpha$. Here, the Bekenstein-Sandvik-Barrow-Magueijo (BSBM) model (which
posits the existence of a scalar field driving evolution in the fundamental
electric charge $e$) is tested against quasar and Planck satellite cosmic
microwave background (CMB) data. In this model, variations in $e$ are coupled
to the matter density through a factor $\zeta_{\rm m}/{\omega}$, which is
related to electromagnetic contributions to nucleon masses, and {the energy}
scale of new physics. Simulations conducted here do not support claims that the
electrostatic contribution to $\zeta_{m}$ is completely shielded. Other common
approximations used in BSBM field evolution are found to be adequate. Principal
components of the CMB data with respect to variations in $\alpha$ are used to
obtain constraints of $\zeta_{\rm m}/{\omega}\lesssim 9.3 \times 10^{-9}$ for a
massless field. A forecast anticipating the promise of the Simons Observatory
(SO) CMB experiment shows that SO will be sensitive to values of $\zeta_{\rm
m}/{\omega}\geq 2.2 \times 10^{-9}$.
