A thin and uniformly positively charged ring of radius R = 0.2 m and net electri

Question

A thin and uniformly positively charged ring of radius R = 0.2 m and net electric charge Q = 5 mC is lying in the x-y plane. The z-axis is perpendicular to the plane of the ring and passes through the center of the ring. If the ring is stationary, the magnetic field at position P is zero, but if the ring is rotating around the z-axis, the magnetic field at position P is not zero. What is the magnitude of the magnetic dipole moment (in Am2 ) of the ring at position P a distance z = 0.5 m above the ring if the ring is rotating around the z-axis with angular frequency omega = 5 rad/s?

(2) A thin and uniformly positively charged ring of radius R = 0.2 m and net electric charge Q = 5 mC is lying in the x-y plane. The z-axis is perpendicular to the plane of the ring and passes through the center of the ring. If the ring is stationary, the magnetic field at position P is zero, but if the ring is rotating around the z-axis, the magnetic field at position P is not zero. What is the magnitude of the magnetic dipole moment (in Am2) of the ring at position P a distance z = 0.5 m above the ring if the ring is rotating around the z-axis with angular frequency = 5 rad/s?

Explanation / Answer

magnetic dipole moment = 1/2 x charge x angular velocity x radius^2

=1/2 x 5 x 10^-3 x 5 x 0.2^2

= 5x10^-4 A.m^2

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