There is an EMF induced in this ring!!
When an electron or proton move in a magnetic field, it doesn't matter if the field is constant or not (relative to all of the ring or cable or coil...etc), THERE WILL ALWAYS BE an EMF = Electro Motive Force acting upon the particles!
See faraday wheel, or homopolar generator: is it not strange that it does work, if you cover the whole surface of the disk with a magnetic field - no changing flux there (for example, a disk magnet with the same diameter), and what is more interesting, that it doesn't matter, if the field is moving together with the disk or not!!?).
What matter is that, where can the forced/accelerated particles go, what path do they have to move, how can you lead them to do work for you.
To understand better lets take it step by step, from the picture above:
Step 1: No field, no current, thats pretty much obvious
Step 2: The ring moving downwards, enter a magnetic field. Electrons at the bottom part get an acceleration, and start to move to the left. There isn't any kind of resistance so they can go to the left - then to the upper part - then down in the right side to arrive at the bottom, where they get the next push. Of course there are many,many,maaany electrons in the wire and they start to move simultaneously, as the first one at the bottom part get the push. It's like a circular water pipe with one pump at one side at the moment of step 2.
Before we move to step 3, it is important to understand this: that in all of the magnetic field the downward moving electrons get an acceleration -lets say- to the left! (or right, for answering the question it doesn't matter if the B-field is into or out of the paper, just understand the complex movement). It means, as long the moving electron is inside the field, it will be accelerated to the left. At the bottom part of the ring, the electrons will be forced to the left, along of the wire. As the ring start to curve upward, the electrons will be forced to the LEFT(outer) side of the wire, they don't get any more EMF to move forward along the wire, meaning upward, instead they get an EMF that force them to the left side of the wire. The new bottom electrons forced left movement will be, what makes our electrons, stopped at the left, move forward again. And this take place in the whole ring. Only the electrons at the bottom part, and the EMF acting upon them will define the current strenght and direction in the ring. [in step 2] (of course, at the right side where electrons 'coming down', they will be forced to the left side as well, meaning to the inner side)
As you move the ring further down, the upper part will enter the magnetic field too. All the electrons in the whole ring will get an EMF forcing them to the left!! But as long it is a changing (growing) magnetic field the bottom part will ALWAYS get a stronger push (from the denser magnetic flux), then the upper -> creating an always net left(clockwise in this case) moving electron stream. It doesn't matter if the flux at the upper part is 0 and at the bottom is +2 or +25 at the upper and +27 at the bottom, you will always get a net LEFT(clockwise) MOVING CURRENT.
Step 3 !: The above explanation are quiet long, so i will be short here, just make the connection yourself.
So at step 3 the upper and bottom part get the same EMF,and while for this reason you see no current in the ring itself, all the electrons are forced to the left. If you connect the ring left side to the right with a wire OUTSIDE of the magnetic field there will be your missed EMF, making an uncomparable current as before. In the example before, you got a field of +25 str. and +27 str. WORKING AGAINST EACH OTHER, producing a net +2 str. EMF, thats pretty sad. While in step3 you got +27 and +27 working together on 2 different part of the ring in paralell. You can't really compare the available current as before.
Step 4 and Step 5 are irrevelant, not helping to answer the question.
Tip: Seems easy, but as you will realise the hardest part in this case (or in all the case with homopolar generators), is HOW to access this enermous current, with high speed motion (for a useful voltage). Changing magnetic flux was always easier to handle...well for a not too good trade-off. The answer for the EMFs for not killing each other in a changing magnetic field might be, cutting the ring in half (upper-lower) and connecting the lower part's left side to the upper part's right side and vice versa...
A muscle man pushing you forward in a free path would be an EMF. The same muscle head pushing you against another man, who gets pushed from the other direction with a geat force... i dont know, but i wouldn't say there is no force 'acting' upon you even though you can't move.. :) [all you have to do, to turn left or right, now there is two of you heading to the same direction with double force] (i don't really recommend a book to use it as any kind of learning reference, that lies to you and can't explain a simple thing like this)