Electric energy and forces in the presence of boundary conditions

Pomer, F.

doi:10.1119/1.15660

Cited by 2 publications

(6 citation statements)

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“…Finally, Ref. [4] treats a similar problem but its approach requires the full Green formalism and is not very easy for practical calculations. By contrast, the formalism presented here only requires the knowledge of the method of images and basic concepts of potential energy.…”

Section: Discussionmentioning

confidence: 99%

“…the values of φ i s and φ f s can be obtained from Eq. ( 5) by utilizing the configuration of images at the beginning and at the end of the process respectively 4 . It is clear that the values of φ f s , φ i s depend on the geometry of the conductor.…”

Section: Simple Applicationsmentioning

confidence: 99%

“…The method of images is a useful tool to calculate electrostatic fields, Green functions and forces that conductors of certain shapes exert over some charges [1]- [3]. However, the internal energy of the configuration is seldom treated by this method [4], and applications are restricted to very special cases [3]. Let us call system A (the real system) the one consisting of a conductor and certain distribution of charges outside it, and system B (the virtual system) the one consisting of the distribution of charges plus the set of image charges, see Fig.…”

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confidence: 99%

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Electrostatic internal energy using the method of images

Díaz¹,

Herrera²,

Niño³

2006

Eur. J. Phys.

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For several configurations of charges in the presence of conductors, the method of images permits us to obtain some observables associated with such a configuration by replacing the conductors with some image charges. However, simple inspection shows that the potential energy associated with both systems does not coincide. Nevertheless, it can be shown that for a system of a grounded or neutral conductor and a distribution of charges outside, the external potential energy associated with the real charge distribution embedded in the field generated by the set of image charges is twice the value of the internal potential energy associated with the original system. This assertion is valid for any size and shape of the conductor, and regardless of the configuration of images required. In addition, even in the case in which the conductor is not grounded nor neutral, it is still possible to calculate the internal potential energy of the original configuration through the method of images. These results show that the method of images could also be useful for calculations of the internal potential energy of the original system.

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Section: Discussionmentioning

confidence: 99%

Section: Simple Applicationsmentioning

confidence: 99%

mentioning

confidence: 99%

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Electrostatic internal energy using the method of images

Díaz¹,

Herrera²,

Niño³

2006

Eur. J. Phys.

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“…There is an apparent factor-of-two discrepancy between the correct answer and the one that many would write down at first sight. This problem has been discussed twice before in American Journal of Physics [4,5], but we believe that this elementary discussion will add to its understanding. In addition we present a non-trivial example of a cubic cavity.…”

mentioning

confidence: 87%

“…with Dirichlet boundary condition G = 0 when r lies on the surface. This is the approach adopted by Pomer [5].…”

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confidence: 99%