Find Vemf (between points 1 and 2) and it's polarity at t = 0. This is a worked out example in my textbook. I have omitted details because my question is specifically on the polarity.

Lenz's law says that an induced electromotive force (emf) always gives rise to a current whose magnetic field opposes the original change in magnetic flux.

Vemf = -dΦ/dt

We first find the flux Φ and Vemf which are function of time. We compute dΦ/dt at t = 0. Then Vemf = -dΦ/dt.

We find that dΦ/dt > 0, so the magnetic field B is increasing. To counter-act this change, I must be in the direction given in the picture. Everything is ok at this point.

Now here is where I get lost. My textbook says:

At t=0, dΦ/dt > 0 and Vemf = -188.5 V. Since the flux is increasing, the current I must be in the direction shown in the figure in order to satisfy Lenz's law. Consequently, terminal 2 is at a higher potential than terminal 1 and Vemf = V1 - V2

I thought I always is from the higher potential to the lower potential. Which should make terminal 1 at a higher potential than terminal 2 considering the direction of I. It seems like the textbook have it backwards.

What am I missing?

 

First off, a voltage inherently has a polarity and so being asked to find the voltage and it's polarity seems redundant.

Put your hand over the loop and just look at the part of the diagram from the two labeled points and to the left. Given the direction of current through that resistor, which point, 1 or 2, has the higher potential?

Now replace the loop with a battery that is oriented so as to produce that same current. Which point is connected to the positive terminal of the battery?

So does whether the current flows through a device from positive to negative or the other way around depend on whether the device is producing or absorbing electrical energy?

Now consider that another name for a loop of wire in a changing magnetic field is an "electric generator".