# Electric field due to changing uniform magnetic field

I think this could be a misunderstanding on my part , still I want to clarify this.Suppose in a region of boundless expanse, there is a uniform magnetic field which changes at a rate $$\frac{d\phi}{dt}$$.I want to find the induced electric field at a certain point so I draw an imaginary circular loop passing through that point.Since the loop and surroundings are similar from all directions the field must be similar at all points of loop too, then from faraday's law $$\int{Edl}=-\frac{d\phi}{dt}$$.I will then take out E because its same for all dl and integrate dl which will be $$2\pi r$$.Now here's the problem , I could've taken any loop , therefore there could've been different radii, and electric field at a point cannot assume multiple values simultaneously, so what's wrong.
I think what I'm taking out common, 'E' is actually a component of field along tangent to the loop , but still I don't know how do the produced electric fields will look like , can someonee please help with these two.