Whenever movement of electrons id produced by a directive force (i.e. a potential difference), a magnetic field is always associated with that movement.
The magnitude and direction of this field depend on the rate of flow of the electrons i.e. the current (1A = 6.02X10⁻ electrons/second) and the direction of such flow.
The shape of the field depends on the path taken by the electrons.
In general, if the electrons travel in a linear path, the magnetic field will be circular in cross-section and if the electrons travel in a circular path, the magnetic field through the path will be linear.