Biot-Savart law indicates that the moving electrons (velocity v) produce a magnetic field B such that

In Biot-Savart's law, magnetic field $\mathrm{B} \left|\right| \mathrm{idl}\times \mathrm{r} \mathrm{and} \mathrm{idl}$ due to flow of electron is in opposite direction of v and by direction of cross product of two vectors, B.
$$\begin{gathered} \mathrm{dB}=\frac{\mathrm{I}\cdot \mathrm{dlsin}\mathrm{\theta }}{{\mathrm{r}}^2} \\ \mathrm{or} \mathrm{dB}=\frac{\mathrm{I}\times \mathrm{dl}}{{\mathrm{r}}^2} \end{gathered}$$
According to Biot-Savart law, if magnetic field is not perpendicular to the motion of charge, then it will not move in helical path, which is not possible for motion of a charge in magnetic field. So, the magnetic field is perpendicular to the direction of flow of charge.