E.3.5 Simple Measurement of B

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 t = Bµsinq. Using the analogy to linear harmonic motion the angular frequency of vibration is

w = _(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.