![]() $Q\frac$ for a given total radiated quantity Q, in spherical coordinates.Īt first I thought of using an oblate spheroid centered at the origin, in either Cartesian or spherical coordinates, with radiation coming from the origin but it's symmetric about the origin (inviting degenerate solutions for this case) and there is such a thing as "oblate spheroid coordinates" (inviting degenerate solutions for this case). Tamer AbuElfadl Curvilinear coordinates (Cylindrical & Spherical) are discussed in detail. In spherical coordinates, we can find the representation of its Dirac delta using the above expression. Zewail City OpenCourseWare 15.6K subscribers Subscribe 1.1K views 2 years ago Electrodynamics I - Dr. Taking a stab in the dark at this, is this correct? Dirac delta: xx' uu' vv' ww' UVW Now this is a very useful result. ![]() It isn't a cylinder, so, were it not for the fact that it is symmetric about the origin (inviting degenerate solutions), and were it not for the fact that it is an oblate spheroid (inviting coordinate transforms involving oblate spheroid coordinates) it would be a generic example as to how to express radiation flux density as a Dirac delta in cylindrical coordinates. What is the general way in which radiation density for a given surface is expressed using Dirac deltas?Ĭonsider this surface expressed in cylindrical coordinates (for any $\phi$ and $r_0$ an oblateness parameter): Del formula edit Table with the del operator in cartesian, cylindrical and spherical coordinates. ![]()
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