The inverse problem for the dipole field

Epp, V.; Janz, Julia

doi:10.1016/j.nimb.2008.02.043

Cited by 2 publications

(4 citation statements)

References 8 publications

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“…In this section, we show that the dipole moment vector cannot be uniquely determined from its electric and magnetic fields. This property was found when solving an inverse problem for the dipole field [7].…”

Section: Transformation Of the Dipole Which Does Not Change Its Elect...mentioning

confidence: 89%

Can a moving charge or a varying dipole produce a constant field?

Boichenko¹,

Epp²,

Janz³

2015

Eur. J. Phys.

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Although the electromagnetic field of a given distribution of charge and current is unambiguously defined by the Maxwell equations, there is no unique inverse correspondence between this field and point-like sources. We prove this statement for electric and magnetic dipoles and discuss two examples when the same field at some point or in some region is generated by either a dipole or an electric charge that are varying in different ways. The electric and magnetic fields of the charge depend on its speed and the distance between the charge and the observation point. It is shown that it is possible to find a law of motion for the charge in which the variation in the distance to the observer is compensated for by variation in the velocity of the charge. One particular example of the motion of a charge is discussed, wherein the electric and magnetic fields at a specific point of observation remain constant. The issues discussed could be of interest to both scientists and scholars.

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Section: Transformation Of the Dipole Which Does Not Change Its Elect...mentioning

confidence: 89%

Can a moving charge or a varying dipole produce a constant field?

Boichenko¹,

Epp²,

Janz³

2015

Eur. J. Phys.

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“…Distance to the dipole can be calculated by formula (13), or (14) or (15). Direction from the dipole to the observer is defined by the unit vector (16), and the dipole polarization vector by (27). Absolute value of the dipole amplitude is given by equations ( 6) and ( 7), because the distance r is already known at this stage.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The same conclusion is applicable to the pair of solutions (31) and (33). Let us estimate errors in the unit vector of direction (16). Using a vector form R = (R 1 , R 2 , R 3 ) we obtain next expression for the differential of n…”

Section: Uniqueness and Stability Of The Solutionsmentioning

confidence: 99%

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Spectral approach to the inverse problem for the field of arbitrary changing electric dipole

Epp

Janz

2013

Inverse Problems in Science and Engineering

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The inverse problem for electromagnetic field produced by arbitrary altered charge distribution in dipole approximation is solved. The charge distribution is represented by its dipole moment. It is assumed that the spectral properties of magnetic field of the dipole are known. The position of the dipole and its Fourier components are considered as the unknown quantities. It is assumed that relative increments of amplitude and phase of magnetic field in the vicinity of the observation point are known. The derived results can be used for study of phenomena concerned with occurrence and variation of localized electric charge distribution, when the position and the dynamics of a localized source of electromagnetic field are to be defined.

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The inverse problem for the dipole field

Cited by 2 publications

References 8 publications

Can a moving charge or a varying dipole produce a constant field?

Can a moving charge or a varying dipole produce a constant field?

Spectral approach to the inverse problem for the field of arbitrary changing electric dipole

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