Given the magnetic field as a vector, how do I find the electric field?
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$\begingroup$ Please provide more explanations about your question. Is the magnetic field time dependent or not? Is it a magnetic field of an electromagnetic wave? $\endgroup$– Mojtaba GolshaniCommented Jul 29, 2014 at 17:29
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1$\begingroup$ Hi user108605. Please don't repost a closed question in a new entry. Instead, you are supposed to edit the original question within the original entry. $\endgroup$– Qmechanic ♦Commented Jul 29, 2014 at 18:48
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2 Answers
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You must known the impedance of the medium. For the vacumm:
$$ \eta_0 = \sqrt{\dfrac{\mu_0}{\varepsilon_0}} $$
then, the relation between the fields:
$$ \vert\mathbf{H}\vert = \dfrac{\vert\mathbf{E}\vert}{\eta_0} $$
in vacumm, of course.
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1$\begingroup$ The impedance is the ratio of the magnitudes of the two vectors, so I don't believe that you can make the assertion your second equation makes. $\endgroup$ Commented Jul 29, 2014 at 17:07
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$\begingroup$ @KyleKanos: Yes. I write the impedance here like a real variable. I tried to provide a guide, rather than an exact solution or an extremely long explanation. $\endgroup$ Commented Jul 29, 2014 at 17:20
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$\begingroup$ The question specifically asks for vectors though, not magnitudes. $\endgroup$ Commented Jul 29, 2014 at 17:22
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$\begingroup$ This is only true for EM waves in a vacuum. $\endgroup$– garypCommented Jul 29, 2014 at 17:49
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$\begingroup$ @garyp : Yes. Maybe the next time I post a comment instead of an answer. Sorry, I just want to give a little help. $\endgroup$ Commented Jul 29, 2014 at 17:55
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$\begingroup$ That would tell me the curl of electric field, not electric field $\endgroup$ Commented Jul 29, 2014 at 16:46
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2$\begingroup$ You obviously can't find the electric field itself because the electric and magnetic fields are independent at each point. $\endgroup$ Commented Jul 29, 2014 at 16:54