ELECTROMAGNET.) Measurement of Magnetic Fields.—The magnetometer method of measuring a field by comparison with a standard field has already been mentioned. It is obviously of very limited applicability. The oscillation method can be used when there is sufficient space for a needle, and the field is sufficiently uniform and not too large (up to about 10 gauss). If the time of oscil lation in a standard field Ho is and the time in the unknown field then The force exerted on a current-bearing conductor may be utilized in a number of ways for measuring a field; for some special purposes it is a very convenient and accurate method. The force on an element ds of a conductor carrying a current i is given by where 0 is the angle between H and ds, and is at right angles to H and ds (see ELECTRICITY). A horizontal field between the poles of a magnet, for example, may be determined by measuring the horizontal force on a vertical wire passing through it by a "pendulum" balance arrangement. The torque exerted on a nar row coil with its plane parallel to the field may also be utilized; by adjusting the current strength and the tension of the suspension, a wide range of field strengths can be measured by comparison with comparable standard fields. Such a device is suitable for determining the intensity in air gaps of magnets.
The most elastic method of measuring fields is based on the fundamental law of electromagnetic induction, that, when the magnetic induction through a circuit changes, an electromotive force, which is proportional to the rate of change of the magnetic induction, is induced in the circuit. Let S be an area bounded by the circuit, dS a small element of that area, and B the normal induction through it. Let N= f BdS. The quantity N is some times known as the magnetic flux through the circuit. Let E be the electromotive force induced when N changes (either due to a change in the field, or a movement of the circuit). Then The total quantity of electricity Q which passes through the cir cuit, when N changes from N1 to N2, is given by If a "search-coil" consisting of n turns of wire is connected in series with a ballistic galvanometer, the resistance of the whole circuit being R, then the quantity of electricity in coulombs, q, which passes through the galvanometer when the coil is removed from a region where the flux linked with each turn is N to a region where the field is zero, is given by If S is the mean effective area of each turn, then N=BS. For free space B=H. If the search coil is reversed in the field, the flux change is double that when it is removed.
Standard search coils, consisting for example of ion turns of fine silk covered wire (No. 4o S.W.G.) on accurately turned marble cylinders some 3 cm. in diameter and 2.5 cm. long, may be constructed so that the number of area-turns can be determined to I part in 2,000. If 0 is the galvanometer throw corresponding to the passage of a quantity of electricity q, then q=KO. The
constant K may be determined from the time of swing, and the deflection for a known steady current, but in practice it is usually more convenient to calibrate the galvanometer directly for ballistic use by sending a known quantity of electricity through it and observing the throw obtained. This may be done by turn ing over a standard coil in a known field; by interrupting or re versing the current in the primary coil of an inductometer, when a calculable quantity of electricity passes through the secondary in series with the galvanometer; with the Hibbert magnetic standard, by allowing a coil to cut through the flux due to a per manent magnet; and by other methods.
In order that a galvanometer may be used ballistically, it is necessary that the time taken for the quantity of electricity to flow through it should be short compared with the time of swing (see ELECTRICAL INSTRUMENTS). In a special form of galvanom eter, the "fluxmeter" due to Grassot, the moving coil, which turns in a strong uniform field, is suspended from a spring sup port by a silk fibre so that the torsional control is practically negligible, and the swings are lim ited mainly by electromagnetic damping influences. A construc tional diagram is shown in fig. 9. The pointer remains almost sta tionary at the limit of its deflec tion, and the readings are inde pendent of the time occupied by the flux change measured. The pointer instrument is portable and convenient, but not so accurate or sensitive as a ballistic gal vanometer.
Search coils for the measurement of H may be constructed in many forms to meet the special requirements, the number of turns necessary depending on the strength of the field and the sen sitivity of the galvanometer. An ordinary circular coil is suitable for many purposes. For measuring the field in which round rods are placed, annular circular coils and saddle shaped coils which fit on the rods may be used, and for flat bars flat coils wound on strips of glass are employed.
The change in the specific resistance of a bismuth wire when placed in a magnetic field may be applied to the measurement of field strength. A useful form of instrument which is supplied commercially, consists of a thin flat spiral of wire. In a typical case the increase of resistance at ordinary temperatures was 17% at 5,000 gauss, 42% at 10,000 gauss. The wire must be calibrated, and for accurate measurements the temperature must be known, owing to the relatively large temperature change in the resistance; also, owing to hysteresis effects, the method is unsuitable for vary ing fields. The method is, however, a most valuable one for measuring strong fields which are uniform over only small regions. Methods for measuring susceptibilities may of course, be applied inversely for the measurement of fields, using a substance whose susceptibility is known. The Quincke capillary rise method for liquids, mentioned later, may often be conveniently used in this way.