<PERSON> gave the right answer. I will just a give a highbrow answer, mostly filled with the jargons:
Potential only makes sense when curl of electric field is zero i.e., $\vec{\nabla}\times\vec{E}=0$, which holds only for electrostatic case. When we have a time changing magnetic field, the right equation is $$\vec{\nabla}\times \vec{E}=-\frac{\partial\vec{B}}{\partial t}$$. Clearly curl of $\vec{E}$ doesn't vanish here, so potential makes no sense here.
What happens if you take a test charge and make it goes around the loop. The force due to electric field is given by $\vec{F}=q\vec{E}$ so work done is $\int\vec{F}\cdot d\vec{l}$ equivalently $$W=q\oint\vec{E}\cdot d\vec{l}$$ where I have used the symbol $\oint$ to denote the work done in completing the loop. You can take another tour around the loop, and you'll spend $2W$ joules. This work done is strikingly different from conservating force work because the latter is zero for a closed-loop.
Electromotive force is defined as $$\oint \vec{f}_s\cdot d\vec{l}$$ where $\vec{f}_s$ is the force responsible for motion of charge after removing electrostatic force since for the latter $\oint \vec{E}\cdot d\vec{l}=0$. 780
In this case electric field produced by changing magnetic field is the sole contributor to $\vec{f}_s$. So there is no issue of going around the loop any times; it is defined only for one round.
Since equipotential lines will make sense only when we have a potential to work on since they simply are $V(x,y)=c$ for some constant $c$. Though if you take radial lines, the work done on the test charge when moved along them is zero since force is perpendicular to the displacement. But it won't suffice they are equipotential lines since there is not potential here. Mathematically, let's say there exists a potential $V$ such that $E=-\vec{\nabla}V$. Then the curl of $\vec{E}$ should give $-\frac{\partial \vec{B}}{\partial t}$ though by identity $$\vec{\nabla}\times\vec{\nabla}V=0.$$ therefore there doesn't exist any scalar potential. Even though there exist paths on which no work is done.
Take an electromagnet run current through it (charging your phone will be enough) and touch the two pointers of the voltmeter so that a closed-loop is formed for current to run through it. You'll read some value and it will change as you change the orientation of loop or loop's shape or loop's distance from the electromagnet. 780