The determination of the constant of a solenoid

Abstract 1. 1. This paper has given a practical method for testing the constant of a solenoid by experimental means. 2. 2. The method recommends itself because of its simplicity. The constant of the solenoid is determined in terms of the deflections of a ballistic galvanometer and the constant of another coil taken as a standard. If a long, slim solenoid is used for the standard, the only quantity which must be known with great accuracy in determining its constant is the number of turns per unit length. The constant of the ballistic galvanometer does not need to be known, neither does the ammeter, which indicates the constancy of the current in the coils, need to be calibrated. Even the exploring coil does not need to have its inductive area determined. Once the constant of the standard coil has been definitely fixed, the method could not be much simpler. 3. 3. It is evident that the exploring coil could have been placed first in one coil and then in the other and the deflection observed when only one field was suddenly reduced to zero. In such a case, S = G d 2 d 1 (4) This last equation appears simpler. The author believes, however, that by keeping the two coils in series it will be easier to keep the current constant, because there is absolutely no change to be made in the circuits except to throw a reversing switch for one coil. Using the coils separately would necessitate change of circuits; also keeping the coils in series insures that in breaking the circuit the field due to both coils must vary simultaneously. Of course, difference in rate of decay of the magnetic fields should not affect the results if the period of deflection of the galvanometer is large enough. 4. 4. An investigation as to what ratio of S G would give the least error in S shows that when S G = 1 the error in S should be a minimum. This is an impossible condition, as the d1 in equation (2) becomes equal to zero. I f the experiment is worked as a zero method it would be necessary to have each coil on a separate circuit and so arranged that the two fields could be made to just neutralize each other. When this occurred there would be no deflection of the galvanometer and equation (2) would then be written: I 1 S − I 2 G = o S = G I 2 I 1 This was tested out, but was not so sensitive as the method finally pursued. In this zero method it would be necessary to know the absolute value of the current, which would mean the calibration of one or two ammeters. 5. 5. This work has shown that great care must be used in winding a solenoid if the constant is to be obtained by computation. The author would recommend concentric “Bakelite” tubes where several layers are to be employed, and the winding carried out similar to the method used by Jenkins. If the constant of the solenoid is to be determined by the method suggested in this paper, then the winding need not be carried out with such extreme care. 6. 6. Investigating the constant of a solenoid has brought out the fact with renewed earnestness that what we work with in a great many experiments is not a uniform field all along the axis of the solenoid, but, as shown by Fig. 4, it is a field that is continually decreasing as one goes from the centre of the coil out toward the ends. In work of measuring the magnetic properties of various substances this is too frequently lost sight of, and in studying such phenomena, as the magnetostrictive effects everyone seems to have fallen into the error of considering the value of the field strength at the centre of the solenoid as holding constant very nearly to the ends. A consideration of the equation for the field strength at any point along the axis of a solenoid will soon convince one of this point, viz., H = 2πn I D+ l 2 (d+ l 2 ) 2 + R 2 − D− l 2 (d+ l 2 ) 2 − R 2 − where D is the distance from the centre of a solenoid of length l and radius R. It was from this equation that the computed values for Fig. 4 were obtained. So far as the author knows no one has done in a practical way for solenoids what Maxwell did for galvanometer coils, viz., determine what the form of a coil should be in order to get certain desired fields. At present work is being done on this problem. It seems quite certain that the field may be kept up to a constant value along the axis much farther from the centre than is now done by ordinary solenoids In closing, expressions of appreciation are due Mr. Ray Calhoon, an advanced student in the department, for the valuable assistance rendered in making long and tedious series of observations.