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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!

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I don't think radial charge gradient matters if you only care about the direction of magnetic field at the center. As long as the disk is negatively charged, you can always consider it to be composed of infinitely many ring currents(with different or same intensities) whose flow directions are all opposite to the rotation. Therefore the direction of the magnetic field will always be the opposite of the angular velocity.

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  • $\begingroup$ But the answer says that magnetic field can be along or opposite to angular velocity vector. It can even be 0. $\endgroup$ – Jaideep stands with Monica Aug 22 '17 at 21:07
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The negative charge on the disc will reorient themselves. Depending on the reorientation the magnetic field may be zero, opposite or in the same direction of angular velocity.

The reason as to why the charges will orient can be thought of as only the electric field can provide the requisite centripetal force and we know by Gauss' law only concentration of negative charges should be more near the center.

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