Electric fields of a uniformly charged elliptical beam

This paper presents results for the electric field due to a uniformly charged elliptical beam in the region outside the beam. Introduction This paper presents results for the electric field due to a uniformly charged elliptical beam outside the beam. Results for the field inside inside the beam are well known [1, 2] The beam being considered extends indefinitly in the z direction and has an elliptical boundary in x and y given by x/a + y/b = 1 (1) The charge density, ρ(x, y, z) is uniform within the elliptical boundary, zero outside the elliptical boundary, and does not depend on z. The results given below depend on the observation made by B. Houssais [3], that the result for the electric field of a gaussian charge distribution given by W. Kellog [1] as a one dimensional integral would hold for any elliptical charge distribution as defined below. This may be stated as follows. Let the charge distribution be given as ρ(x, y, z) = λn(x, y) (2)