Published on *UCLA Physics & Astronomy* (https://demoweb.physics.ucla.edu)

An undamped compass needle vibrates about equilibrium in a B-field; the vibration frequency can be used as a measure of B. Let the (unknown) moment of inertia of the compass needle be I, and its (unknown) magnetic moment μ. Then the restoring torque τ=Bμsinθ. Using the analogy to linear harmonic motion the angular frequency of vibration is

ω = √ (k/m) = √ (Bμ/I)

Thus, the frequency of vibration of the needle is proportional to √B. Measure the frequency of vibration of the compass needle in the Earth's field of 0.5 gauss, and obtain the strength of other B-fields from these results.

**Gauss Meter**

Accurate and detailed measurements of B-field can be made with a Gaussmeter and Hall probe. You can illustrate the size of the gauss unit and the strength of various magnets, or make measurements of B-fields for electron deflection, etc.