Kraftfreie Magnetfelder II

Die allgemeine Lösung der Differentialgleichung der kraftfreien Magnetfelder wird für den zylindersymmetrischen Fall angegeben. Die Energiedichte des Magnetfeldes kann als Funktion des Abstandes von der Symmetrieachse vorgegeben werden, sie muß nur zwei Ungleichungen befriedigen. Die Komponenten des magnetischen Feldvektors und der elektrischen Stromdichte folgen dann durch Differentiation. Durch Konstruktion eines Beispiels wird gezeigt, daß ein solches Feld Impuls und Drehimpuls in Richtung der Achse transportieren kann in einem Ausmaß, das durch den Gesamtstrom und den gesamten magnetischen Fluß nicht bestimmt ist.The general solution of the differential equation of force-free magnetic fields is given in the case of cylindrical symmetry. The energy density has to fulfil two inequalities; apart from this, it can be freely chosen as function of the distance from the axis of symmetry. The components of the field as well as the electric current density follow from it purely by differentiation. By explicitly constructing a three-parameter family of such force-free fields it is shown that the amount of momentum and of angular momentum transported by the field in the direction of the axis is not determined by the total magnetic and electric flux of the field.

Download Full-text

Exposure to electric or magnetic fields in the low and intermediate frequency range. Methods for calculating the current density and internal electric field induced in the human body

10.3403/03219456u ◽

2015 ◽

Keyword(s):

Magnetic Fields ◽

Electric Field ◽

Current Density ◽

Human Body ◽

Intermediate Frequency ◽

Internal Electric Field ◽

Frequency Range

Download Full-text

Exposure to electric or magnetic fields in the low and intermediate frequency range. Methods for calculating the current density and internal electric field induced in the human body

10.3403/bsen62226-3 ◽

2015 ◽

Keyword(s):

Magnetic Fields ◽

Electric Field ◽

Current Density ◽

Human Body ◽

Intermediate Frequency ◽

Internal Electric Field ◽

Frequency Range

Download Full-text

Exposure to electric or magnetic fields in the low and intermediate frequency range. Methods for calculating the current density and internal electric field induced in the human body

10.3403/bsen62226-2 ◽

2015 ◽

Keyword(s):

Magnetic Fields ◽

Electric Field ◽

Current Density ◽

Human Body ◽

Intermediate Frequency ◽

Internal Electric Field ◽

Frequency Range

Download Full-text

Exposure to electric or magnetic fields in the low and intermediate frequency range. Methods for calculating the current density and internal electric field induced in the human body

10.3403/bsen62226 ◽

2015 ◽

Keyword(s):

Magnetic Fields ◽

Electric Field ◽

Current Density ◽

Human Body ◽

Intermediate Frequency ◽

Internal Electric Field ◽

Frequency Range

Download Full-text

The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses

Advances in Mathematical Physics ◽

10.1155/2017/3094173 ◽

2017 ◽

Vol 2017 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Xianzhen Zhang ◽

Zuohua Liu ◽

Hui Peng ◽

Xianmin Zhang ◽

Shiyong Yang

Keyword(s):

Differential Equation ◽

Integral Equation ◽

General Solution ◽

Differential Equations ◽

Fractional Differential Equations ◽

Fractional Derivatives ◽

Order System ◽

Impulsive Systems ◽

Fractional Differential ◽

Noninstantaneous Impulses

Based on some recent works about the general solution of fractional differential equations with instantaneous impulses, a Caputo-Hadamard fractional differential equation with noninstantaneous impulses is studied in this paper. An equivalent integral equation with some undetermined constants is obtained for this fractional order system with noninstantaneous impulses, which means that there is general solution for the impulsive systems. Next, an example is given to illustrate the obtained result.

Download Full-text

The stability of force-free magnetic fields with cylindrical symmetry in the context of solar flares

Solar Physics ◽

10.1007/bf00155164 ◽

1968 ◽

Vol 3 (2) ◽

pp. 298-315 ◽

Cited By ~ 86

Author(s):

Ulrich Anzer

Keyword(s):

Magnetic Fields ◽

Solar Flares ◽

Cylindrical Symmetry ◽

The Stability

Download Full-text

Hamiltonian description of ion motion in crossed electric and magnetic fields with cylindrical symmetry

Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms ◽

10.1016/0168-583x(92)95493-b ◽

1992 ◽

Vol 64 (1-4) ◽

pp. 353-357

Author(s):

J.I.M. Botman ◽

H.L. Hagedoorn

Keyword(s):

Magnetic Fields ◽

Cylindrical Symmetry ◽

Hamiltonian Description ◽

Ion Motion ◽

Electric And Magnetic Fields

Download Full-text

Approximate analytical solution for the propagation of shock wave in a mixture of small solid particles and non-ideal gas: isothermal flow

Zeitschrift für Naturforschung A ◽

10.1515/zna-2021-0196 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Gorakh Nath

Keyword(s):

Shock Wave ◽

Analytical Solutions ◽

Order Approximation ◽

Fluid Pressure ◽

Strong Shock ◽

Cylindrical Symmetry ◽

Solid Particles ◽

Approximate Analytical Solutions ◽

Axis Of Symmetry ◽

Physical Variables

Abstract This paper presents the development of mathematical model to obtain the approximate analytical solutions for isothermal flows behind the strong shock (blast) wave in a van der Waals gas and small solid particles mixture. The small solid particles are continuously distributed in the mixture and the equilibrium conditions for flow are maintained. To derive the analytical solutions, the physical variables such as density, pressure, and velocity are expanded using perturbation method in power series. The solutions are derived in analytical form for first approximation, and for second order approximation the set of differential equations are also obtained. The effects of an increase in the problem parameters value on the physical variables are investigated for first order approximation. A comparison is also, made between the solution of cylindrical shock and spherical shock. It is found that the fluid density and fluid pressure become zero near the point or axis of symmetry in spherical or cylindrical symmetry, respectively, and therefore a vacuum is created near the point or axis of symmetry which is in tremendous conformity with the physical condition in laboratory to generate the shock wave.

Download Full-text