I was trying to solve this question:
I understand that if the current is increasing leftward, then via Lenz's Law, the direction of the induced EMF will be to the right. Given that I now know the direction of EMF, how can I figure out which point is at a higher potential?
For a resistor you know that the (conventional) current flows from the higher potential to the lower potential but that is not necessarily true for an inductor.
To answer your question it is perhaps easier not to consider the inductor in isolation but rather as part of a complete circuit as shown below.
In the left hand diagram the current in the circuit is increasing and the potential of node $a$ is zero and that of node $b$ is $\mathcal E = iR$.
Since $\mathcal E > iR$ the potential of node $b$ is higher than that of node $a$.
In the right hand circuit the current through the inductor is decreasing and the potential of node $a$ is again zero but the potential of node $b$ is $-iR$.
In this case, the potential of node $b$ is lower than that of node $a$.
First keep in mind that current flow by convention is the flow of positive charge, that is, from higher to lower potential.. So what does that tell you about the polarity across the inductor, that is, which side is the positive (higher potential) side? You also know the voltage across an inductor will change in the direction so as to oppose a change in current. So what does that tell you about how the voltage is changing, I.e. is the positive side getting more positive or less positive?
Hope this helps.
