# How large of a radius can a closed loop around a changing magnetic field get for it to still experience an induced emf from Faraday's Law?

I was wondering about the graph of the emf around a changing magnetic field for all radii of a closed loop centered at the changing magnetic field.

Here is what I think.

$$\textrm{emf} = -~\frac{\mathrm d\phi_B}{\mathrm dt}$$

And if we assume that the magnetic field that is changing has a radius of R, then it would become:

$$\textrm{emf} = -~A \frac{\mathrm dB}{\mathrm dt} = -~\pi R^2\frac{\mathrm dB}{\mathrm dt}$$

Now, if we were inside the magnetic field with a radius r < R, then the equation would be:

$$\textrm{emf} = -~ \pi r^2 \frac{\mathrm dB}{\mathrm dt}$$ which means that $\textrm{emf} \propto r^2$

But when we are outside the magnetic field with a radius r > R, then the equation would be:

$\textrm{emf} = -~ \pi R^2 \frac{\mathrm dB}{\mathrm dt}$ which means that Emf is constant for all r > R. Is this true? If I have a closed loop with a super super long radius, will there still be a potential on that loop? The equation $V = Ed$ certainly agrees, but that doesn't make sense to me? Are there any limits to Faraday's Law? Any help is much appreciated!