Calculations
We are going to use Biot-Savart
$$\Delta \bar B = \frac{\mu_0}{4\pi} \frac{I \Delta\bar l\times \hat r}{r^2}$$.
I have used books such as "Matter and Interactions 3rd Edition" by Chabay (particularly pages around 721) and "Introduction to Electrodynamics" by Griffiths (particularly pages around 78 and around 322).
3A
What is the induced EMF?
$\frac{dB}{dt}=35 mT/s$
Assume $\frac{dB}{dt}:=\frac{\partial B}{dt}$. Now by Faraday's law
$\nabla\times \bar E = -\frac{\partial\bar B}{\partial t}$ and now by
Stokes -theorem:
$$emf=\oint\bar E\cdot d\bar l = -\int\int_A \frac{\partial\bar B}{dt}\cdot d\bar A \\=-\frac{\partial\bar B}{dt} 20^2$$
so $$ emf =-\frac{\partial\bar B}{dt} 20^2 (cm)^2=-(20cm)^2 35 mT/s$$
Griffiths about the page 322 covers this issue, reading... history with something about the magnetic field and Biot-Savart but not apparently needed for this question.
TODO 1: how can I get the electric field?
TODO 2: how can I get the current?
Other questions in the attachment
3B: potential between corners assuming static-field -approximation
$$V(\bar r)=\oint\bar E\cdot d\bar l$$ where $\theta\in[0,\pi/2]$ and, since potential does not depend on the path, you can choose any
path like along the circle the easy one. Use the solution of $\bar E$
from the 3A.
3C: "Dynamic field cannot precisely be approximated with static potential, why?"
Because changing magnetic field have different characteristics to static fields such as the inductance. (Not sure, perhaps some better explanation exist).
Conclusion
Todo.
