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This question is an exact duplicate of:

Given the magnetic field as a vector, how do I find the electric field?

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marked as duplicate by Qmechanic Jul 29 '14 at 18:46

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Please provide more explanations about your question. Is the magnetic field time dependent or not? Is it a magnetic field of an electromagnetic wave? – Mojtaba Golshani Jul 29 '14 at 17:29
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. – Qmechanic Jul 29 '14 at 18:48

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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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. – Kyle Kanos Jul 29 '14 at 17:07
@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. – Martin Petrei Jul 29 '14 at 17:20
The question specifically asks for vectors though, not magnitudes. – Kyle Kanos Jul 29 '14 at 17:22
This is only true for EM waves in a vacuum. – garyp Jul 29 '14 at 17:49
@garyp : Yes. Maybe the next time I post a comment instead of an answer. Sorry, I just want to give a little help. – Martin Petrei Jul 29 '14 at 17:55

You are probably looking for Maxwell equations.

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That would tell me the curl of electric field, not electric field – user108605 Jul 29 '14 at 16:46
You obviously can't find the electric field itself because the electric and magnetic fields are independent at each point. – Luboš Motl Jul 29 '14 at 16:54

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