![]() ![]() Do not forget to add the proper units for electric flux. Finally, the imaginary distribution is projected to the receiver surface along the reflection direction by image mapping. In general, the integral for the flux is difficult to evaluate, and Gauss’ Law can only be used analytically in cases with a high degree of symmetry. The symmetry of the Gaussian surface allows us to factor outside the integral. With the proper Gaussian surface, the electric field and surface area vectors will nearly always be parallel. Second, a convolution integral is conducted on the image plane to depict an imaginary radiative flux distribution and an analytical function with a closed-form expression is derived. Evaluate the integral over the Gaussian surface, that is, calculate the flux through the surface. These integrals turn up in subjects such as quantum field theory. Multiply the magnitude of your surface area vector by the magnitude of your electric field vector and the cosine of the angle between them. ![]() The n + p = 0 mod 2 requirement is because the integral from −∞ to 0 contributes a factor of (−1) n+ p/2 to each term, while the integral from 0 to +∞ contributes a factor of 1/2 to each term.
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