I'm given that vec(E)=(mu_0 p_0 omega^2)/(4 pi r) [cos u(hat(x)-x/r hat(r))+sin u(hat(y)-y/r hat(r))] implies -(mu_0 p_0 omega^2)/(4 pi r) [cos u hat(x) xx hat(r) + sin u hat(y) xx hat(r)]=(1)/(c) hat(r) xx vec(E)

Jaqueline Velez 2022-09-24 Answered
I'm given that
E = μ 0 p 0 ω 2 4 π r [ cos u ( x ^ x r r ^ ) + sin u ( y ^ y r r ^ ) ]
implies
μ 0 p 0 ω 2 4 π r [ cos u x ^ × r ^ + sin u y ^ × r ^ ] = 1 c r ^ × E ,
but I don't follow how to get from the former to the latter.
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Answers (1)

berzamauw
Answered 2022-09-25 Author has 9 answers
You get the second equation by taking the cross product of the first one with 1 c r ^ on the left and remembering that x × x = 0 , so in particular r ^ × r ^ = 0 ; and also that r ^ × x ^ = x ^ × r ^
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