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# Magnetic energy

About: Magnetic energy is a research topic. Over the lifetime, 14640 publications have been published within this topic receiving 273627 citations.

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TL;DR: In this article, an investigation of the structure of the electromagnetic field near the focus of an aplanatic system which images a point source is made, and the results are illustrated by diagrams and in a tabulated form based on data obtained by extensive calculations on an electronic computor.

Abstract: An investigation is made of the structure of the electromagnetic field near the focus of an aplanatic system which images a point source. First the case of a linearly polarized incident field is examined and expressions are derived for the electric and magnetic vectors in the image space. Some general consequences of the formulae are then discussed. In particular the symmetry properties of the field with respect to the focal plane are noted and the state of polarization of the image region is investigated. The distribution of the time-averaged electric and magnetic energy densities and of the energy flow (Poynting vector) in the focal plane is studied in detail, and the results are illustrated by diagrams and in a tabulated form based on data obtained by extensive calculations on an electronic computor. The case of an unpolarized field is also investigated. The solution is riot restricted to systems of low aperture, and the computational results cover, in fact, selected values of the angular semi-aperture a on the image side, in the whole range 0 ≤ α ≤ 90°. The limiting case α → 0 is examined in detail and it is shown that the field is then completely characterized by a single, generally complex, scalar function, which turns out to be identical with that of the classical scalar theory of Airy, Lommel and Struve. The results have an immediate bearing on the resolving power of image forming systems; they also help our understanding of the significance of the scalar diffraction theory, which is customarily employed, without a proper justification, in the analysis of images in lowaperture systems.

2,636 citations

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TL;DR: In this paper, the diffraction of electromagnetic radiation by a hole small compared with the wave-length is treated theoretically, and a complete solution is found satisfying Maxwell's equations and the boundary conditions everywhere.

Abstract: The diffraction of electromagnetic radiation by a hole small compared with the wave-length is treated theoretically. A complete solution is found satisfying Maxwell's equations and the boundary conditions everywhere (Section 4). The solution holds for a circular hole in a perfectly conducting plane screen, but it is believed that the method will be applicable to much more general problems (Section 8). The method is based on the use of fictitious magnetic charges and currents in the diffracting hole which has the advantage of automatically satisfying the boundary conditions on the conducting screen. The charges and currents are adjusted so as to give the correct tangential magnetic, and normal electric, field in the hole. The result (Section 5) is completely different from that of Kirchhoff's method, giving for the diffracted electric and magnetic field values which are smaller in the ratio (radius of the hole/wave-length) (Section 6). The diffracted field can be considered as caused by a magnetic moment in the plane of the hole, and an electric moment perpendicular to it (Section 6). The theory is applied to the problem of mutual excitation of cavities coupled by small holes (Section 9). This leads to equations very similar to those for ordinary coupled circuits. The phase and amplitude relations of two coupled cavities are not uniquely determined, but there are two modes of oscillation, of slightly different frequency, for which these relations are opposite (Section 10). The problem of stepping up the excitation from one cavity to another is treated (Section 11).

2,562 citations

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TL;DR: In this paper, the authors developed analytical relationships and computations of power dissipation in magnetic fluid (ferrofluid) subjected to alternating magnetic field and showed that the dissipation results from the orientational relaxation of particles having thermal fluctuations in a viscous medium.

Abstract: This study develops analytical relationships and computations of power dissipation in magnetic fluid (ferrofluid) subjected to alternating magnetic field. The dissipation results from the orientational relaxation of particles having thermal fluctuations in a viscous medium.

2,111 citations

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TL;DR: In this paper, it was shown that two oppositely directed sunspot fields with scales of 104 km could be merged by Sweet's mechanism, if shoved firmly together, in about two weeks; their normal interdiffusion time would be of the order of 600 years.

Abstract: Sweet's mechanism for the merging of two oppositely directed magnetic fields in a highly conducting fluid is investigated in a semi-quantitative manner. It is shown that two oppositely directed sunspot fields with scales of 104 km could be merged by Sweet's mechanism, if shoved firmly together, in about two weeks; their normal interdiffusion time would be of the order of 600 years. It is suggested that Sweet's mechanism may be of considerable astrophysical importance: It gives a means of altering quickly the configuration of magnetic fields in ionized gases, allowing a stable field to go over into an unstable configuration, subsequently converting much of the magnetic energy into kinetic energy of the fluid.

1,562 citations