A nonconducting rod of mass M and length ? has a uniform charge per unit length ? and rotates with angular velocity ? about an axis through one end and perpendicular to the rod.

(a) Consider a small segment of the rod of length dx and charge dq = ? dx at a distance x from the pivot (Figure). Show that the magnetic moment of this segment is ½??x2 dx.

(b) Integrate your result show that the total magnetic moment of the rod is ? = 1/6 ??? 3.

(c) Show that the magnetic moment m and angular momentum L are related by m = (Q/2M)L, where Q is the total charge on the rod.

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dx