Scattering of an Electromagnetic Pulse by a Moving Wedge

An Extension of the Kelvin Image Theory to the Conducting Heaviside Ellipsoid

“…where x 0 , y 0 , z 0 satisfy Equation (9). Now replacing n and E in Equation (15) by expression (16) and the sum of the fields (18)- (20), one obtains that σ is given by Equation (13), as it should be.…”

“…where x 0 , y 0 , z 0 satisfy Equation (9). A little reflection, making use of the uniqueness theorem in the Σ frame, reveals the physical meaning of the second term in expression for σ (13): it is the surface charge distribution which shields the interior of the Heaviside ellipsoid from the electromagnetic field of the comoving charge q. Consequently, the first term in (13) is the surface charge density on an isolated Heaviside ellipsoid (9) carrying a charge Q + qa/b; as it is well known, it is the same charge density one would have if an isolated conducting ellipsoid with the same total charge and of the same geometric shape were at rest in Σ [4,25,26].…”

“…One can easily find the outward unit normal n at a given point of the ellipsoidal surface (9). Namely, introducing f (x 0 , y 0 , z 0 ) = γ 2 x 2 0 + y 2 0 + z 2 0 − a 2 , equation of the Heaviside ellipsoid becomes f (x 0 , y 0 , z 0 ) = 0.…”

“…where x 0 , y 0 , z 0 satisfy Equation (9). On the other hand, the electric field outside the moving spheroid (9) is the sum of the electric fields E q , E Q+qa/b and E −qa/b due to the uniformly moving charges q, Q + qa/b and −qa/b, respectively.…”

“…(The famous examples are Einstein's calculation of the radiation pressure of a monochromatic plane linearly polarized electromagnetic wave on a perfect plane mirror in uniform motion [3,5,6] and Poincaré's derivation of the electromagnetic field due to a uniformly moving point charge [7,8].) While the Frame Hopping Method is the standard research tool (cf, e.g., [9][10][11][12]), simple illustrations of the method in applications to the as yet unsolved problems seem to be lacking in the literature. So in this paper we present a generalization of the Kelvin image theory for a conducting sphere in the field of a point charge to the case of a moving spheroidal conductor in the field of a comoving charge.…”