How Does Lenz's Law Determine Induced Current Direction?

[hurtfree1]

Homework Statement

An electromagnet is placed next to a coil of wire. According to Lenz’s law, what will be the direction of the induced current in the resistor R in the following cases?
a. the magnetic field suddenly decreases after the switch is opened
b. the coil is moved closer to the electromagnet

In many transformers, the wire around one winding is thicker, and therefore has lower resistance, than the wire around the other winding. If the thicker wire is wrapped around the secondary winding, is the device a step-up or a step-down transformer? Explain.

Homework Equations

I don't think we have to use an equation for both of the problems.

The Attempt at a Solution

OK, the file I attached is the diagram for the first one;
I was thinking (a. the induced current will change its direction toward the elctromagnet.) (b. nothing would change) but I really don't understand Lenz's Law and it's really confusing for me. I know what Lenz's Law is stating, but I really don't get how "the magnetic field would oppose change."
The second one, I know the resistance and all that depends on the wire's length, but I don't have any clue why the thickness of the wire matters.
Please help me out (:

 

[kuruman]

Hi hurtfree1, welcome to PF. Here are a couple of questions to ponder about.

In part (a) is the current in the resistor attached to the coil flowing left to right or right to left in order to "oppose change"?

In part (b), if you wrap thicker wire in the secondary, do you get a higher or a lower number of turns per unit length than in the primary?