Magnetic field calculations with a uniform external field as the excitation typically formulate boundary value problems using scalar magnetic potentials. However, for eddy current magnetic fields and similar problems, the vector magnetic potential must be employed as the governing potential function. Currently, there are no published literature reports on the method for setting boundary conditions for uniform magnetic fields using the vector magnetic potential. To address this, this paper proposes two boundary condition application methods based on vector magnetic potential. The analytical solutions for the magnetic field are derived using the separation of variables method, and then finite element magnetic field simulations are conducted. Both analytical calculations and numerical simulations demonstrate that the proposed boundary conditions generate uniformly distributed magnetic flux density. The findings provide references for eddy current magnetic field simulations under uniform timevarying magnetic field excitations.