Just apply the Lorentz's force \vec{F}=q\vec{v}\times\vec{B} to your simulation.
For B field in z direction, velocity in x-y plane.
F_x=q*v_y*B_z
F_y=-q*v_x*B_z
or the differential equations are
\frac{d^2v_x}{dt}=\frac{q}{m}v_y*Bz
\frac{d^2v_y}{dt}=-\frac{q}{m}v_x*Bz

And you can check out whether v=\sqrt{v_x*v_x+v_y*v_y} is a constant or not.