Magnetometer
Magnetic fields are vector quantities characterized by both strength and direction. The strength of a magnetic field is measured in units of tesla in the SI units, and in gauss in the cgs system of units. 10,000 gauss are equal to one tesla. Measurements of the Earth's magnetic field are often quoted in units of nanotesla (nT), also called a gamma. The Earth's magnetic field can vary from 20,000 to 80,000 nT depending on location, fluctuations in the Earth's magnetic field are on the order of 100 nT, and magnetic field variations due to magnetic anomalies can be in the picotesla (pT) range. "Gaussmeters" and "teslameters" are magnetometers that measure in units of gauss or tesla, respectively. In some contexts, magnetometer is the term used for an instrument that measures fields of less than 1 millitesla (mT) and gaussmeter is used for those measuring greater than 1 mT.
Planck constant
The gyromagnetic ratio "γ" is the constant of proportionality between the frequency "ν" of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field . It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring "B", but the value for protons in water at is known to better than one part per million. The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, "γ"′. The gyromagnetic ratio is related to the shielded proton magnetic moment "μ"′, the spin number "I" ( for protons) and the reduced Planck constant.
The ratio of the shielded proton magnetic moment "μ"′ to the electron magnetic moment "μ" can be measured separately and to high precision, as the imprecisely known value of the applied magnetic field cancels itself out in taking the ratio. The value of "μ" in Bohr magnetons is also known: it is half the electron g-factor "g". Hence
A further complication is that the measurement of "γ"′ involves the measurement of an electric current: this is invariably measured in "conventional" amperes rather than in SI amperes, so a conversion factor is required. The symbol "Γ"′ is used for the measured gyromagnetic ratio using conventional electrical units. In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases. Only the high-field value "Γ"′(hi) is of interest in determining the Planck constant.
Substitution gives the expression for the Planck constant in terms of "Γ"′(hi):