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I have a situation where there exist a time varying magnetic field and a circular loop place perpendicular to it. Let us assume that the magnetic field is $\vec B=\frac{B_0 t}{\tau}$ . I tried to modify this problem is my own way that I will be discussing later right now is irrelevant. Also please note, the minor details of this problem need not be considered like polarization etc, or anything, think of it as high school level stuff.

So, my question is that, I know that by using Faraday law $e=-\frac{d\phi}{dt}$

I will get the result as $e=-\pi r^2 \frac{dB}{dt}$(not substituting value yet as it's not required).

So, now i have got this emf whose meaning i don't understand, what I mean to say is what would this emf look like , what would be it's direction, end point , start point, etc. Basically I can't understand it's physical sense and direction(loosely speaking here , please note that this direction, i meant to be associated with the path integral).

Also, suppose that I replace the situation with an circuit having equivalent emf what would it look like?

Now continuing with the problem by the $e=-\vec E.\vec dl$ , I was told that there exist a induced electric field having circular loop and direction I don't remember but with upward magnetic field seems to be anti-clockwise(please verify and explain!)

Gives $E=\frac{1}{2}r\frac{dB}{dt}$ so, the only problem is how I can visualize this emf and electric field. As well is there any way to produce current using that emf? Connecting somewhere? Or an equivalent circuit?

EDIT: The equation of electric field of course implies that $E$ is constant for a given $r$ , so this implies the circular nature of electric field but what about it's direction, suppose that if i connect a wire loop in that electric field would a current flow through it, would that be the direction of emf? (Suppose that material is not affected by magnetic field).

Someone
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  • emf is NOT a conservative field. Do you know how to deal with that or is that your question? – CuriousOne May 02 '15 at 21:13
  • No. I do not that the induced emf is not conservative that's why the closed integral along a loop of arc length $2\pi r$ was not 0 so the field is not conservative. But I can't seem to get an idea for a equivalent circuit for e,g its very easy in motional emf you just have to use Fleming right hand rule. Also I do not understand the exact physical sense of this emf. – Someone May 03 '15 at 05:09
  • The non-conservative nature of the field is the cause of the non-existence of an "equivalent circuit" for it (in the sense of nodes and node potentials). How much potential difference one gets out of this field depends on the number of turns that one takes around any given area. That's how transformers work: same field trough the primary and secondary coil, different number of turns, different voltage. One can visualize the field with closed field lines, but the important quantity is always the flux trough a closed curve AND the number of turns we take around that closed curve. – CuriousOne May 03 '15 at 05:17
  • Interesting ! I never thought of that it can't be took by an equivalent circuit. Well you see , If you'd see a lot of problem in some Indian books. You can see them replaced the emotional emf by an equivalent cell and measure force on it – Someone May 03 '15 at 05:45
  • I really hate mobile. Motional* and replacing* can you elaborate this a little more and put it in answer so I can up vote? – Someone May 03 '15 at 05:46
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    Did you try to search for "non-conservative field" on stackexchange? Lots of people have written useful answers on the topic. – CuriousOne May 03 '15 at 05:53

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