Advanced Problem on Magnetics

[zorro]

Homework Statement

A charge Q is uniformly distributed on the ring which is free to rotate about a light horizontal rod. The rod is suspended by light inextensible strings and a magnetic field B is applied as shown in the figure. The initial tensions in the strings are To. If the breaking strength of each string is 3To/2, find the maximum angular velocity w with which the wheel can be rotated.

The Attempt at a Solution

I want to clear some doubts before proceeding with the solution-
It is given that the ring is free to rotate about the rod. Is the ring attached to the rod by another rod? If yes then does the former rod rotate with it?
What causes the tension to change in the strings?

 

[hikaru1221]

It is given that the ring is free to rotate about the rod. Is the ring attached to the rod by another rod? If yes then does the former rod rotate with it?

If you don't know, who knows?

What causes the tension to change in the strings?

I assume that the ring is like a wheel. When the wheel turns, there is torque due to magnetic field. Thus, the wheel gets unbalanced. It has to finds a new equilibrium position, which corresponds to a new tension in the string.

 

[zorro]

I assume that the ring is like a wheel. When the wheel turns, there is torque due to magnetic field. Thus, the wheel gets unbalanced. It has to finds a new equilibrium position, which corresponds to a new tension in the string.

The magnetic field is vertically upwards (say along + Y axis) and the direction of magnetic moment is along the rod ( say along +X axis).
So torque acts in the positive z-direction and it causes the ring to rotate about this z-axis.
So the ring will tilt about the z-axis, hit the rod and stop in that place. How will that even change equilibrium?

 

[hikaru1221]

Okay. Think about some "realistic" set-up. Imagine that the ring = a flat round disk with a hole at the center, through which the rod passes. So the ring can rotate freely about the rod, with the rod as the axis of rotation. When the torque due to B-field is applied, it lifts both the ring and the rod. Then...?

 

[zorro]

Do you mean that the tension in one of the strings will be greater than T while it will be less than T in another string due to the 'lifting effect' of torque?

 

[hikaru1221]

Or perhaps the other string is not even stretched

 

[zorro]

OK. I will try it now.

 

[zorro]

I figured out the solution.
If there is a change in tension in one of the strings, there must be a change in tension in the other string ( for translational equilibrium ). So there is no point of other sting not gettting stretched.
Thanks a lot for giving it a start!