Current and Ohm's Law in Motional EMF examples

Question:

What causes the current to flow through the whole circuit in the given example? I understand that on the disk there is an emf (integral of force per unit charge) from the centre of the disk to the edge ($0$ to $a$) but unlike a stationary circuit with a battery, where you have an induced electric field all around the circuit, causing the current to move around the circuit, I don't see why the current flows outside the circuit in this case? Is it maybe due to particles bumping into each other or is there in fact an electric field around the circuit?

Also what justifies Ohm's law in the form $I = \frac{\mathcal{E}}{R}$, I understand Ohm's law is derived from the case where you have two points maintained a potential difference and some sort of a resistor in between, as described here, and in this case $V = \mathcal{E}$. But I don't see how any of this translates to this example?

Thanks for any assistance.