# Oscillations in a magnetic field

1. Mar 10, 2009

### w3390

1. The problem statement, all variables and given/known data
A long, narrow bar magnet that has magnetic moment $$\vec{\mu}$$ parallel to its long axis is suspended at its center as a frictionless compass needle. When placed in a region with a horizontal magnetic field $$\vec{B}$$, the needle lines up with the field. If it is displaced by a small angle theta, show that the needle will oscillate about its equilibrium position with frequency f= (1/2pi)*sqrt(uB/I), where I is the moment of inertia of the needle about the point of suspension.

2. Relevant equations
No specific equations

3. The attempt at a solution
I remember from my mechanics physics class that I need to figure out what the restoring force is. However, that is where I run into my first problem. I do not know how to model an equation to show how the magnetic field will restore the magnet to equilibrium.

2. Mar 10, 2009

### w3390

This equation looks the exact same as the equation for the oscillation frequency of a spring f=(1/2pi)*sqrt(k/m). I know it is a harmonic oscillator, but can anyone get me started on how to change from sqrt(k/m) to sqrt(uB/I). Any help on how to start would be greatly appreciated.

Last edited: Mar 10, 2009