A SURFACE INTEGRAL IN POTENTIAL THEORY

Geophysics ◽  
1970 ◽  
Vol 35 (3) ◽  
pp. 501-503
Author(s):  
Gunnar Bodvarsson
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Potential Theory ◽  
Short Note ◽  
One Dimension ◽  
Surface Integral ◽  
Gravity Method ◽  
Long Time ◽  
Acceleration Of Gravity ◽  
Surface Integrals

In potential theory it is often convenient to transform volume integrals over homogeneous bodies into surface integrals. The suppression of one dimension will in general simplify the calculation of the integrals. For a long time this technique has been used in magnetic field theory and the transformation is given in standard texts on potential theory (see MacMillan, 1930, section 55). The transformation appears less well known to authors concerned with the gravity method. The purpose of the present short note is to give an example of the application of this technique, a technique which appears to lead to results of practical value in the computation of the acceleration of gravity due to given bodies.

scholarly journals Difficulties in learning the introductory magnetic field theory in the first years of university

2004 ◽  
Vol 88 (3) ◽  
pp. 443-464 ◽  
Author(s):  
Jenaro Guisasola ◽  
José M. Almudí ◽  
José L. Zubimendi
Keyword(s):  
Magnetic Field ◽  
Field Theory

scholarly journals Broadband Linear Polarization in Ap Stars

1993 ◽  
Vol 138 ◽  
pp. 305-309
Author(s):  
Marco Landolfi ◽  
Egidio Landi Degl’Innocenti ◽  
Maurizio Landi Degl’Innocenti ◽  
Jean-Louis Leroy ◽  
Stefano Bagnulo
Keyword(s):  
Magnetic Field ◽  
Circular Polarization ◽  
Linear Polarization ◽  
Rotation Axis ◽  
Spectral Lines ◽  
Line Of Sight ◽  
Long Time ◽  
Rotating Star ◽  
Ap Stars ◽  
The Magnetic Field

AbstractBroadband linear polarization in the spectra of Ap stars is believed to be due to differential saturation between σ and π Zeeman components in spectral lines. This mechanism has been known for a long time to be the main agent of a similar phenomenon observed in sunspots. Since this phenomenon has been carefully calibrated in the solar case, it can be confidently used to deduce the magnetic field of Ap stars.Given the magnetic configuration of a rotating star, it is possible to deduce the broadband polarization at any phase. Calculations performed for the oblique dipole model show that the resulting polarization diagrams are very sensitive to the values of i (the angle between the rotation axis and the line of sight) and β (the angle between the rotation and magnetic axes). The dependence on i and β is such that the four-fold ambiguity typical of the circular polarization observations ((i,β), (β,i), (π-i,π-β), (π-β,π-i)) can be removed.

A NONPERTURBATIVE CALCULATION FOR THE EFFECTIVE POTENTIAL OF THE $\left(\frac{g}{4}\phi^{4}-J\phi\right)_{1+1}$ SCALAR FIELD THEORY USING THE OSCILLATOR REPRESENTATION METHOD WITH BOREL RESUMMATION

2007 ◽  
Vol 22 (06) ◽  
pp. 1265-1278
Author(s):  
ABOUZEID M. SHALABY ◽  
S. T. EL-BASYOUNY
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Phase Transition ◽  
Scalar Field ◽  
External Magnetic Field ◽  
Effective Potential ◽  
Oscillator Representation ◽  
Constructive Field Theory ◽  
Representation Method ◽  
Oscillator Representation Method

We established a resummed formula for the effective potential of [Formula: see text] scalar field theory that can mimic the true effective potential not only at the critical region but also at any point in the coupling space. We first extend the effective potential from the oscillator representation method, perturbatively, up to g3 order. We supplement perturbations by the use of a resummation algorithm, originally due to Kleinert, Thoms and Janke, which has the privilege of using the strong coupling as well as the large coupling behaviors rather than the conventional resummation techniques which use only the large order behavior. Accordingly, although the perturbation series available is up to g3 order, we found a good agreement between our resummed effective potential and the well-known features from constructive field theory. The resummed effective potential agrees well with the constructive field theory results concerning existing and order of phase transition in the absence of an external magnetic field. In the presence of the external magnetic field, as in magnetic systems, the effective potential shows nonexistence of phase transition and gives the behavior of the vacuum condensate as a monotonic increasing function of J, in complete agreement with constructive field theory methods.

Thermodynamics of Bidisperse Ferrofluids in Zero External Magnetic Field: Theory and Simulations

2015 ◽  
Vol 233-234 ◽  
pp. 331-334
Author(s):  
Anna Yu. Solovyova ◽  
Ekaterina A. Elfimova
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Free Energy ◽  
External Magnetic Field ◽  
Volume Concentration ◽  
Helmholtz Free Energy ◽  
Hard Spheres ◽  
Particle Volume ◽  
Simulation Data ◽  
Theoretical Predictions

The thermodynamic properties of a ferrofluid modeled by a bidisperse system of dipolar hard spheres in the absence of external magnetic field are investigated using theory and simulations. The theory is based on the virial expansion of the Helmholtz free energy in terms of particle volume concentration. Comparison between the theoretical predictions and simulation data shows a great agreement of the results.

A Proof of the Biot-Savart Law

1968 ◽  
Vol 72 (689) ◽  
pp. 437
Author(s):  
B. G. Newman
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Electromagnetic Field ◽  
Fluid Mechanics ◽  
Small Length ◽  
Line Vortex ◽  
Line Current ◽  
Electromagnetic Field Theory ◽  
The Magnetic Field

The Biot-Savart law gives the velocity associated with an elemental portion of line vortex, or the magnetic field associated with an elemental portion of line current. The following proof may appeal to students who approach fluid mechanics or electromagnetic-field theory from the engineering viewpoint. It will be stated in terms of fluid mechanics. Consider a very small length δs of line vortex of circulation strength Γ. At P(x) the velocity δV associated with this portion depends on Γ δs and x.

scholarly journals A Physically-Motivated Quantisation of the Electromagnetic Field on Curved Spacetimes

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 844
Author(s):  
Ben Maybee ◽  
Daniel Hodgson ◽  
Almut Beige ◽  
Robert Purdy
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Quantum Field Theory ◽  
Electromagnetic Field ◽  
Minkowski Space ◽  
Unruh Effect ◽  
Quantum Field ◽  
Rindler Space ◽  
Electric And Magnetic Field ◽  
Curved Spacetimes

Recently, Bennett et al. (Eur. J. Phys. 37:014001, 2016) presented a physically-motivated and explicitly gauge-independent scheme for the quantisation of the electromagnetic field in flat Minkowski space. In this paper we generalise this field quantisation scheme to curved spacetimes. Working within the standard assumptions of quantum field theory and only postulating the physicality of the photon, we derive the Hamiltonian, H ^ , and the electric and magnetic field observables, E ^ and B ^ , respectively, without having to invoke a specific gauge. As an example, we quantise the electromagnetic field in the spacetime of an accelerated Minkowski observer, Rindler space, and demonstrate consistency with other field quantisation schemes by reproducing the Unruh effect.

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