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why does iime varying magnetic field produce electric field(or vice versa) in adjacent space rather than in same space?
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I assume that's supposed to be 'time varying' sorry if I got your hopes up, I can't answer it effectively, but it's a good questions so I want to see the answer.
yes *time varying
...and by adjacent, I'm guessing you mean perpendicular to, rather than parallel to?
yes, they are perpendicular but also adjacent(that's why they propagates)
I still don't understand your sense of the word "adjacent". The picture I have in my mind is this one: http://micro.magnet.fsu.edu/primer/java/wavebasics/basicwavesjavafigure1.jpg
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induced field is ahead of the source field in the direction of propagation.
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