We have recently finished the chapter on Electromagnetic Induction and it was only in the last week that I finally got the hang of the part about induced electric field. My book in its intensely concise and simple language states:
A time varying magnetic field produces an induced electric field.
Now that we have started upon the chapter not-so-modern Physics and I am doing a bit of side reading I found out that space and time are basically one and the same thing/two sides of the same coin/(Insert any other metaphor you prefer)
So since time and space are sort of one thing shouldn't a space varying magnetic field also produce an electric field.
Best Answer
What matters is the rate of change of the magnetic flux through a closed loop (or an open surface): $$ {\cal E}=-\frac{d}{dt}\int_C \vec B\cdot d\vec S $$ It doesn't matter how this change in flux is produced.
You can start, for instance, with a static magnetic field produced by a wire carrying a constant current, and drag a square frame at constant speed away from this wire, and the result will be a change in flux, and thus an EMF, and thus an associated electric field. In this case, the change in flux is produced by the change in the strength of $\vec B$ over the frame when the frame is moved, even if $\vec B$ is not time-varying.
Alternatively, you can have a fixed frame but a time-dependent $\vec B$ so that $\vec B\cdot d\vec S$ changes in time. You can also deform the frame in a constant magnetic field so the change in flux is not contained in the changing $d\vec S$. You can also change the angle between $\vec B$ and $d\vec S$ at some rate so that $\vec B\cdot d\vec S$ changes in time .
All of the above result in induction, and thus in an EMF, and thus in an electric field.