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Does electric field caused by time varying magnetic field form closed loops(electric field starts from a positive charge and ends at a negative charge)? and are they conservative or non-conservative fields?

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Are you asking if this is always the case, or for an example where this is the case? –  DJBunk Feb 20 '13 at 20:30
    
May be related to my answer to physics.stackexchange.com/q/5573/520 (or rather a comment under it). Short answer is "yes", but if you didn't believe me the first time there doesn't seem to be much point in repeating myself. –  dmckee Feb 20 '13 at 21:45
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The field lines certainly can form closed loops, for example in a transformer. But they don't have to either, an example being a plane EM wave.

For a specific example, consider the following long solenoid of radius $a$ and turn density $n$ with a time-varying current running through it: $I(t)$.

enter image description here

The solenoid is oriented along the x-axis, and current runs in the direction of $-x$ to $+x$. This current induces a magnetic field inside the solenoid:

$$\mathbf{B}=\mu_0 nI(t) \mathbf{i}$$

Now, by Faraday's Law:

$$\int \mathbf{E} \cdot \mathrm{d} \mathbf{s}=-\frac{\partial}{\partial t} \int \mathbf{B} \cdot \mathrm{d} \mathbf{A}$$

Which gives us a relationship the time derivative of magnetic flux through a loop and the electric field along that loop. Using a loop that is concentric with the solenoid gives:

$$2\pi r E=-\frac{\partial}{\partial t} \int \mu_0 n I(t) \mathrm{d}A=-\mu_0 n I'(t) \pi a^2$$

$$\Rightarrow E=-\frac{1}{2}\mu_0 n a^2~ \frac{I'(t)}{r}$$

where $I'(t)=\partial I / \partial t$, and we know $E$ is oriented along a closed loop.

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In high school physics, it's given that electric field starts from a positive charge and ends at a negative charge, does the above mentioned field follow the same? –  vpp Feb 21 '13 at 14:36
    
No. The electric field around the solenoid looks similar to the magnetic field around straight current. I.e. it looks similar to the field in: school-for-champions.com/science/images/… . –  elfmotat Feb 21 '13 at 15:48
    
What is the difference between this field and the one caused by static charges?? –  vpp Feb 21 '13 at 15:54
    
The way E fields are generated is given to us by Maxwell's equations, and the equation for finding the E field produced by a charge and the equation for finding the E field produced by a changing B field are different. –  elfmotat Feb 21 '13 at 16:02
    
Are these non-conservative or conservative fields?? –  vpp Feb 22 '13 at 4:46
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