A disk of radius R carries a fixed charge density and rotates with angular velocity .

A disk of radius R carries a fixed charge density σ and rotates with angular velocity ω.

(a) Consider a circular strip of radius r and width dr with charge dq. Show that the current produced by this strip dI = (ω/2π) dq = ωσr dr.

(b) Use your result from part (a) to show that the magnetic field at the center of the disk is B = ½μ0σωR.

(c) Use your result from part (a) to find the magnetic field at a point on the axis of the disk a distance x from the center.