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Magazine Chapter 4: Q64P (page 917)
A plastic circular loop has radius R, and a positive charge q is distributed uniformly around the circumference of the loop. The loop is then rotated around its central axis, perpendicular to the plane of the loop, with angular speed v. If the loop is in a region where there is a uniform magnetic field directed parallel to the plane of the loop, calculate the magnitude of the magnetic torque on the loop.
Short Answer
The magnitude of the magnetic torque on the loop is.
Step by step solution
Definition of magnetic field
The term magnetic field may be defined as the area around the magnet behave like a magnet.
Determine the magnitude of the magnetic torque on the loop.
The moving charged loop create current, so loop treated as circular wire where current I moving through it and the T be the period of the rotation. Than
But
So
l = qf
And
So
Due to magnetic field the torque acting on the loop is
is the angle between magnetic field and magnetic moment which is
And
So
But
So
Hence, the magnitude of the magnetic torque on the loop is .
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