<p>An exact two-dimensional, time-dependent solution for the evolution of the magnetic field during nearly spherically symmetric accretion has been derived. This solution is based on Newtonian dynamics and considers the Keplerian and sub-Keplerian flows around a black hole, within the Schwarzschild metric. In this paper, we also discuss the possible origins of large-scale magnetic fields around black holes. For example, such strong large-scale magnetic fields could originate in the interstellar medium or in a companion star external to the accretion disk, and be advected inward by the accreting plasma, growing over time. The findings show that the uniform magnetic field of a subsonic flow, initially weak at infinity, grows with time and evolves into a quasi-radial configuration, a behavior found in both flow types. We also find that the growth of the radial component of magnetic field is more pronounced in the sub-Keplerian than in Keplerian flow. However, for both types of flows, the magnetic field does not reach saturation for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(r&gt; r_{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>&gt;</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>. Instead, it continues to grow until the disk evolves from its initial state toward a configuration approaching a magnetically arrested disk, forming a sub-magnetically arrested disk state.</p>