A negatively charged metallic disk rotates about an axis passing through its centre perpendicular to it's plane. Can the magnetic field generated by the disk on its axis near the centre be in the direction of angular velocity? Can it be zero?

Since the disk is metallic, charge should spread uniformly on its surface. So magnetic field should always be opposite to angular velocity. But, on second thoughts, it is possible that due to the rotation, the electrons experience a centrifugal force which creates some kind of radial charge gradient. Or may be the magnetic field generated by one of the elemental ring (which together constitute the disk) applies force on the other rings, which again takes me to the same thought of a radial charge gradient, but this time inwards.

How should I think further to come to any conclusions?

Thank you!

A negatively charged metallic disk rotates about an axis passing through its centre perpendicular to its plane. Can the magnetic field generated by the disk on its axis near the centre be in the direction of angular velocity? Can it be zero?

Since the disk is metallic, charge should spread uniformly on its surface. So magnetic field should always be opposite to angular velocity. But, on second thoughts, it is possible that due to the rotation, the electrons experience a centrifugal force which creates some kind of radial charge gradient. Or it may be that the magnetic field generated by one of the elemental ring (which together constitute the disk) applies force on the other rings, which again takes me to the same thought of a radial charge gradient, but this time inwards.

How should I think further to come to any conclusions?

Thank you!