volume | PIER Journals

2007-01-31

The Magnetic-Moment Quadric and Conditions of Vanishing Magnetic Moment for a Rotational Charged Body

Guo-Quan Zhou,

Dr. Guo-Quan Zhou

Department of Physics

Wuhan University

China

Homepage

Wen-Jun Zhou

Dr. Wen-Jun Zhou

School of Electrical Engineering

Wuhan University

China

Homepage

, Vol. 70, 211-223, 2007

doi:10.2528/PIER07011201

Abstract

Based on the concept of charge moment tensor T̃ which is different from the existent electric multiple-moment, and the concept of principal axes and principal-axis scalar charge moment, the condition of zero magnetic moment for an arbitrary rotational body with given charge distribution has been given explicitly in this paper. We find the loss of positive definiteness of T̃ is its most important characteristic which forms a sharp contrast with that of its mechanic counterpart - the positive definite inertia tensor of rigid bodies. Meanwhile the relationship between the quadric distributive law of magnetic moment and the parameters of tensor T̃ is discussed in detail. Accordingto the theory of analytic geometry, we give a series of test formulae, classify and enumerate every kind of possible quadric in a table. Finally, conclusion is given that any rotation axis which passes through origin O and alongwith any of the asymptotic line of the quadric (hyperboloids or hyperbolic cylinders) can lead to a vanishingmag netic moment.

Citation

Copy Export

Guo-Quan Zhou, and Wen-Jun Zhou, "The Magnetic-Moment Quadric and Conditions of Vanishing Magnetic Moment for a Rotational Charged Body," , Vol. 70, 211-223, 2007.
doi:10.2528/PIER07011201

References

1. Xu, D.-F. and Z.-S. Yu, "The calculation of magnetic moment for a rotational charged body rotating around a fixed axis," University Physics, Vol. 16, No. 4, 3-4, 1997.

2. Zhou, G.-Q., "Charge moment tensor and the magnetic moment of rotational charged bodies," Progress In Electromagnetics Research, Vol. 68, 156-160, 2007.

3. Zhou, G.-Q., "Several rules about the magnetic moment of rotational charged bodies," Progress In Electromagnetics Research Symposium, Vol. S2007 in Beijing, 2007.

4. Zhou, G.-Q., "Principles and examples about calculatingthe magnetic moment of rotational charged bodies," Physics and Engineering, Vol. 14, No. 2, 16-19, 2004.

5. Liu, J.-P., Electrodynamics, 153-165, 153-165, 2004.

6. Lim, Y. K., Introduction to Classical Electrodynamics, World Scientific, 1986.

7. Tchernyi, V. V., et al. "possible electromagnetic nature of the Saturn's rings: superconductivity and magnetic levitation," Progress In Electromagnetics Research, Vol. 52, 277-299, 2005.
doi:10.2528/PIER04082801

8. Capozzoli, A., et al. "Global optimization and antennas synthesis and diagnosis, part one: concepts, tools, strategies and performances," Progress In Electromagnetics Research, Vol. 56, 195-232, 2006.
doi:10.2528/PIER04123001

9. Bellett, P. T., et al. "An investigation of magnetic antennas for ground penetrating radar," Progress In Electromagnetics Research, Vol. 43, 257-271, 2003.
doi:10.2528/PIER03051301

10. Dmtriev, V., "Tables of the second rank constitutive tensors for linear homogeneous media described by point magnetic groups of symmetry," Progress In Electromagnetics Research, Vol. 28, 43-95, 2000.
doi:10.2528/PIER99062502

11. Yin, W.-Y., et al. "The Mueller matrix of a two-layer eccentrically bianisotropic cylinder linear array with double helical conductances of the surfaces: classification of the magnetic symmetry groups," Progress In Electromagnetics Research, Vol. 30, 105-130, 2001.
doi:10.2528/PIER00031303

12. Dai, H., Theory of Matrices, 149-159, 75-77, 2001.

13. Tismennetsky, L. P., The Theory of Matrices with Applications, 2nd edition, 1985.

14. Pearson, C. E., Handbook of Applied Mathematics, 64-70, 45-46, 1974.