# How to calculate the electric field generated from a changing magnetic field without a wire

Say we have this situation: where there's a magnetic field inside an imaginary circle with radius r (which means there is no wire!). There's a change in magnetic field over time which means that the flux is also changing. Say we want to calculate the electric field in any point in space, with radius bigger or smaller than r.

My first guess would be to use faraday's law:

But isn't that law just for a circuit/wire? I know that the left side of the equation is just \begin{align} 2\pi ER &&\text{(not r)}\ \end{align} and from there we would be able to calculate $E$. But is this valid?

Aditional question: say that circle is now an actual copper wire for example, and we use that law to calculate the EMF. Will there still be an electric field outside that wire too? I guess so but I want to be sure.