The scaling law for the horizontal length scale
$\ell$ relative to the domain height
$L$, originating from the linear theory of quasi-static magnetoconvection,
$\ell /L \sim Q^{-1/6}$, has been verified through two-dimensional (2-D) direct numerical simulation (DNS), particularly at high values of the Chandrasekhar number (
$Q$). This relationship remains valid within a specific flow regime characterized by columnar structures aligned with the magnetic field. Expanding upon the
$Q$-dependence of the horizontal length scale, we have derived scaling laws for the Nusselt number (
$Nu$) and the Reynolds number (
$Re$) as functions of the driving forces (Rayleigh number (
$Ra$) and
$Q$) in quasi-static magnetoconvection influenced by a strong magnetic field. These scaling relations,
$Nu \sim Ra/Q$ and
$Re \sim Ra Q^{-5/6}$, have been successfully validated using 2-D DNS data spanning a wide range of five decades in
$Q$, ranging from
$10^5$ to
$10^9$. The successful validation of the relations at large
$Q$ values, combined with our theoretical analysis of dissipation rates and the incorporation of the horizontal length scale's influence on scaling behaviour, presents a valid approach for deriving scaling laws under various conditions.