  The intensity of the far-ultraviolet (FUV; 6-13.6 eV) interstellar radiation
field (ISRF) in galaxies determines the thermal and chemical evolution of the
neutral interstellar gas and is key for interpreting extragalactic observations
and for theories of star-formation. We run a series of galactic disk models and
derive the FUV ISRF intensity as a function of the dust-to-gas ratio,
star-formation rate density, gas density, scale radius, and observer position.
We develop an analytic formula for the median FUV ISRF flux. We identify two
dimensionless parameters in the problem: (1) the dimensionless galactic radius,
$X$, which measures the radial extent of FUV sources (OB stellar associations)
in the disk; (2) the opacity over the inter-source distance, $\tau_{\star}$,
which measures the importance of dust absorption. These parameters encapsulate
the dependence on all of the physical parameters. We find that there exists a
critical $\tau_{\star}$, or equivalently a critical dust-to-gas ratio,
$Z_{d,{\rm crit}}' \approx 0.01-0.1$ the Milky Way value, at which the ISRF
changes behavior. For $Z'_d>Z_{d,{\rm crit}}'$ the ISRF is limited by dust
absorption. With decreasing $Z'_d$, the ISRF intensity increases as more
sources contribute to the flux. For $Z'_d < Z_{d,{\rm crit}}'$ the ISRF
saturates as the disk becomes optically thin. We find that the ISRF per
star-formation rate density in low metallicity systems, such as dwarf and high
redshift galaxies, is higher by up to a factor of 3-6 compared to their
Milky-Way counterparts. We discuss implications to the potential mechanisms
that regulate star-formation in low metallicity galaxies.
