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4. For a steady-state charge distribution and divergence-free current distribution the electric and magnetic fields E(r, y, z and H(z, y, z) satisf,y Here ρ = p(z, y, z) and J(z, y, z) are assumed to be known. The radiation that the fields produce through a surface S is determined by a radiation flux density vector field, called the Poynting vector field, a) If S is a closed surface, show that the radiation flux (that is, the flux of P through S) is given by where V is the region enclosed by S b) Examples of such fields are In this case, find the flux of the Poynting vector through the hemispherical shell shown in Figure 4. (Notice that it is an open surface.) x2 +y2+2=25 Figura 4: The surface for Exencise 4b) c) The fields of part b) produce a Poynting vector field passing through the toroidal surface shown in Figure 5. What is the flux through this torus? Figura 5: The surface for Exercse 4c)

especialmente el punto C

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Answer 1

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