  We investigated the diagnostic potential of the Stokes $V$ profile of the
H$\alpha$ line to probe the chromospheric line-of-sight (LOS) magnetic field
($B_{\mathrm{LOS}}$) by comparing the $B_{\mathrm{LOS}}$ inferred from the weak
field approximation (WFA) with that of inferred from the multi-line inversions
of the Ca II 8542 {\AA}, Si I 8536 {\AA} and Fe I 8538 {\AA} lines using the
STiC inversion code. Simultaneous spectropolarimetric observations of a pore in
the Ca II 8542 {\AA} and H$\alpha$ spectral lines obtained from the SPINOR at
the Dunn Solar Telescope on the 4th of December, 2008 are used in this study.
The WFA was applied on the Stokes $I$ and $V$ profiles of H$\alpha$ line over
three wavelength ranges viz.: around line core ($\Delta\lambda=\pm0.35$ {\AA}),
line wings ($\Delta\lambda=[-1.5, -0.6]$ and $[+0.6, +1.5]$ {\AA}) and full
spectral range of the line ($\Delta\lambda=\pm1.5$ {\AA}) to derive the
$B_{\mathrm{LOS}}$. We found the maximum $B_{\mathrm{LOS}}$ strengths of
$\sim+800$ and $\sim+600$ G at $\log\tau_{\mathrm{500}}$ = $-$1 and $-$4.5,
respectively in the pore. The morphological map of the $B_{\mathrm{LOS}}$
inferred from the H$\alpha$ line core is similar to the $B_{\mathrm{LOS}}$ map
at $\log\tau_{\mathrm{500}}$ = $-$4.5 inferred from multi-line inversions. The
$B_{\mathrm{LOS}}$ map inferred from the H$\alpha$ line wings and full spectral
range have a similar morphological structure to the $B_{\mathrm{LOS}}$ map
inferred at $\log\tau_{\mathrm{500}}$ = $-$1. The $B_{\mathrm{LOS}}$ estimated
from H$\alpha$ using WFA is weaker by a factor of $\approx 0.53$ than that of
inferred from the multi-line inversions.
