Um campo elétrico no espaço livre, em coordenadas esféricas, é dado por �⃗� ????(????) = ????0(????)????−???????????????? ???? V/m. a. Calcule �⃗⃗� , assumindo que o c...

Question

Um campo elétrico no espaço livre, em coordenadas esféricas, é dado por �⃗� ????(????) = ????0(????)????−???????????????? ???? V/m. a. Calcule �⃗⃗� , assumindo que o comportamento de onda plana uniforme; b. Calcule a média temporal do vetor de Poynting; c. Expresse a potência externa média em watts através de uma concha esférica fechada de raio r, centrada na origem.

Ed · Answer

a. Para calcular o vetor campo elétrico �⃗⃗�, é necessário aplicar a equação de onda plana uniforme em coordenadas esféricas. O resultado é:

�⃗⃗� = ????0(????)????−????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

b. Para calcular a média temporal do vetor de Poynting, é necessário utilizar a equação:

???? = 1/2Re(�⃗� × �⃗⃗�*)

Onde * representa o conjugado complexo. O resultado é:

???? = ????0^2(????)^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^2????^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Um campo elétrico no espaço livre, em coordenadas esféricas, é dado por �⃗� ????(????) = ????0(????)????−???????????????? ???? V/m. a. Calcule �⃗⃗� , assumindo que o c...

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