V.G. Sapogin, N.N. Prokopenko, V.I. Marchuk

The analytical method for calculation of magnetic characteristics of conducting ring with finite radial width has been proposed. The method permits: 1) to calculate the radial distribution of magnetic fields, being formed in the internal and external spaces of the ring by direct current; 2) to evaluate the value of magnetic flux, intersecting the internal surface of the ring; 3) to calculate the inductance, coupling the magnetic flux and the current, forming this flux, via the ring; 4) to find the frequency dependence of Q-quality and define the scales of characteristic frequencies. The method, used to calculate the magnetic fields of conducting ring, shows that the magnetic field inside geometric conductor has the same singularity as the field of linear geometric conductor. The magnetic field out of conducting geometric ring has the same singularity nearby the ring. The field decreases inversely as the cube of distance at the large distances from the ring. The analytic form of flux inductance for the ring has been obtained. It is followed from this form that the case of inductances, which are small in comparison with the scale, is realized in the ring under the small values of orifice-s radius. Appropriately, the case of large inductances is realized in the ring under the large values of orifice-s radius. The comparison of theoretical results with experimental one points out at the discrepancy of results for some times. It can be explained by the fact that running inductance of lead wire has not been taken into account. But this running inductance depends on the length of lead wire and can be more than inductance of the ring for some times. The calculation of Q-quality of ring-s flux inductance points out at its dependence of the frequency. Q-quality becomes more than unity under the frequency upper than lower frequency limit.

 

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