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I think any changing magnetic field will create/induce an electric field through empty space. Is that correct? And if so, what is the direction of the field? I mean, the electric field vectors must have *some* direction, but I can't possibly imagine which direction that should be. Everything I try gives me some sort of contradiction. I also read that this electric field is "not conservative". I don't really understand what is meant by this and how it can be "not conservative", can someone please clarify?

And how can you find the magnitude of the electric field? For example, in the concrete situation where B varies as [tex]B = B_0 \sin \omega t[/tex] - how do I calculate E?? I can calculate the time derivative of the flux through some imaginary closed loop, but whenever I try to calculate E, I get some weird result.

Could someone please explain? I really don't understand this stuff.