Measurement

Next we must consider how magnetic field is measured. Field-measuring instruments are known as ‘gaussmeters’ (10⁴ gauss =1 tesla). The magnitude and direction of a uniform, steady field can be determined absolutely using a search coil or a rotating-coil fluxmeter (Fig. 1). The principle is that a transient or alternating emf ε is induced according to Faraday’s law, which follows from

ε = −NdΦ/dt, .........(1)

where N is the number of turns on the coil of area A. The flux density in air B₀ = Φ/A is deduced by integrating the emf, B₀ = (1/NA) ∫ Edt as the search coil is removed from the uniform field to a region where the field is zero. When measuring a pulsed field, there is no need to move the coil. Likewise, a coil rotating about an axis perpendicular to B₀ generates an alternating emf ε =−NAωB₀sinωt. These measurements are absolute, but inconvenient.

Figure 1: Some methods of measuring magnetic fields: (a) search coil, (b) rotating coil fluxmeter, (c) Hall probe and (d) nuclear magnetic resonance probe.

In practice, a Hall effect or magnetoresistance sensor is generally used to measure magnetic field. The active area of the semiconducting Hall probe is of order 1 mm², and it generates a voltage V_H = B₀I/n_cet, where I is the sensing current, t is the thickness of the semiconductor and n_c is the carrier density. The probe needs to be calibrated, and possibly corrected for temperature fluctuations, but the Hall voltage is linear in magnetic field. Accuracy is about 1%. Magnetoresistance sensors, can be based, for example, on spin valves with crossed anisotropy. Like fluxgate sensors, which depend on the asymmetric saturation of soft magnetic wires or thin-films elements, they are good for fields below 100 A m⁻¹ but they have the advantage of a high bandwidth.
Much greater accuracy and precision is possible by measuring the NMR frequency of rubidium vapour, for example, which is ν =13.93 MHz T⁻¹ for the ⁷⁷Rb nucleus, or even water, where the resonance frequency is 42.58 MHz T⁻¹ for the H nucleus, better known as the proton.