Let us consider a small magnetic needle of magnetic moment m, and moment of inertia I, placed in a uniform magnetic field B. If the needle is suspended in the field, and allowed to oscillate, then it will experience a restoring couple \(\tau\) = mBsinθ .
Hence, we can write
For small value of θ , we have sin θ ≈ θ .
Thus the (small amplitude) oscillations (of a magnetic needle) are simple harnonic with a time period given by
This expression is often used for an accurate determination of B.
Proceeding, exactly on the same lines, as we studied in electrostatics, we can obtain the magnetic potential energy, Um , of a magnet, in a magnetic field.
We then have
