A hypothetical model of confinement in a dia-electric medium

The assumption of a perfect color dia-electric vacuum in quantum chromodynamics (QCD) led to a reasonable explanation of quark confinement. Along the same lines, a hypothetical dia-electric medium in electromagnetism is shown to lead to charge confinement; although such a medium does not exist, the analysis of this hypothetical problem illuminates in a very simple and straightforward way how this dia property (negative susceptibility) of a medium leads to confinement. It is shown that adding a dipole (particle-antiparticle) charge distribution to such a dia-electric medium would lead to the creation of a cavity surrounding the charges; by a simple analysis, using the image problem along with a series expansion in Legendre polynomials, it is shown that the polarization charge distribution on the cavity's surface would lead to an increase in the dipole energy by a finite amount; on the other hand, the increase in the electric energy of a single charge inserted in such a medium would be infinite. It is thus concluded that in such a dia-electric medium, separating the charges of a dipole would require an infinite amount of energy, and thus illustrating in a simple way the confinement concept. (orig.)