Current Loop Model Research Articles

Palaeosecular variation and the current loop model of the geomagnetic field

The geomagnetic palaeosecular variation has been studied in terms of two current loops which change their positions and orientations with time. The results broadly agree with the observed data. Comparison with the existing models is made.

Current loop models of the Earth's magnetic field

Eleven models of the earth's magnetic field, of a new kind, were derived. They are based on sets of circular loops of filamentary electric current (current loops). Seven of the models consist of one to seven current loops that were constrained to lie on the surface of the earth's core. The other four models consist of one to four unconstrained current loops. The magnetic field of current loops was evaluated by numerical approximation of the Biot‐Savart formula. The parameters of the models were estimated by least squares using 412 uniformly distributed field vectors representing the observed field at 1975. The Marquardt nonlinear least squares method was used. Twenty preliminary computer runs, using randomly determined initial parameter values, were made for each model. Of the eleven models derived, only the one consisting of two unconstrained current loops is significantly more efficient than spherical harmonic analysis of comparable order at representing the static field. In the models consisting of four or fewer core‐surface current loops, the radii of the loops are greater than 2655 km. The currents flow generally westward and range in magnitude from 0.5 to 1.9 GA. The other core‐surface current loop models have, in addition, a small‐radius current loop in the western hemisphere and an eastward flowing current. In the models consisting of unconstrained current loops all the currents are located below the surface of the core. Their radii range from 812 to 2984 km.

Conventions for Magnetic Quantities in SI

Magnetic equations written in International Standard (SI) units usually use either the Sommerfeld convention (m = IA, H = B/μ0−M) or the Kennelly convention [m′ = μ0IA, H = 1/μ0(B−M′)]. An alternative is the “SI electric” convention (m = IA, H = B−μ0M) proposed by Stopes-Roe. In this paper it is shown that the “SI electric” convention arises naturally from the comparison of pole and current loop models for magnetic materials, and hence overcomes the problems of illogical factors of μ0 inherent in the Sommerfeld and Kennelly formulations. This approach clarifies the roles of the field vectors B and H.

Current loops models in magnetism

The derives some of the well known formulae used in magnetism by simple current loop models.

Force on a conducting current loop

There has been some discussion about whether the force on a current loop in a time-variant electromagnetic field is different from the force on a magnetic-charge dipole. Several workers have concluded that the force is the same. In this paper, this conclusion is reinforced by a calculation of force in a class of conducting current-loop models. We show that the force is the same as that calculated by simpler means for a magnetic-charge dipole of the same magnetic moment.