# Magnetic rod in Magnetic Field [closed]

How does thin magnetic rod suspended in uniform magnetic field oscillate? I want to know what kind of oscillations will they be (displacement will be angular or linear) and which phenomenon (what forces are involved) causes these oscillations? And why it has to be thin?

For example:

In a spring block system, SHM is carried out for small linear displacements. And this motion is due to restoring forces of spring.

Some formulations would be appreciated.

## closed as unclear what you're asking by ZeroTheHero, AccidentalFourierTransform, Yashas, Jon Custer, John RennieApr 1 '17 at 7:00

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• I think you are missing something. Does it really need to be thin? – Utkarsh futous Mar 31 '17 at 14:10
• I think it may be a more complex phenomenon, I suggest to write more from it. It would be really unfortunate if your question would be closed as unclear, because it is interesting. – peterh Mar 31 '17 at 15:18
• @Utkarsh I came across this question twice and the same was mentioned i.e. it needs to be thin, in both of them. I can attach a picture of that question, if required – killer JONES Apr 3 '17 at 2:39

## 1 Answer

There will be a magnetic moment induced in the rod. For a small angle displacement from stable equilibrium, the torque $\tau=m\times B=mB*sin(\theta)\approx mB\theta$

This, when equated with the product of the rod's moment of inertia and angular acceleration will give a differential equation that shows that the rod will oscillate.

• Like i asked does it really have to be thin ? – Utkarsh futous Mar 31 '17 at 14:42
• I can't think of any reason why it should have to be thin, but there might be a reason that I don't see. – GeeJay Mar 31 '17 at 15:51