Lenz's Law and Cantilevers

[skeletalclown]

Hey, I've got a SAC on electromagnetism coming up soon, but I'm still pretty confused by Lenz's Law. I understand the basic theory of opposing magnetic fields, but im having trouble with the more complex examples such as this one. So yeah, i was just wondering if someone could give me a bit of a detailed solution to this attached problem (I'm mostly having trouble visualising how the magnetic fields interact in three dimensions).



I'm also having quite a lot of trouble with Structures/Materials cantilever problems (even their basic theory), and would love any advice.

[speedy]

Firstly you have to ask yourself - what is changing? In this case force is being applied externally.

6a. We must take the right side of the rod (because it is entering the field first). The force is being applied to the right, we need to oppose this, according to Lenz's law - the force will be to the left.  So we point our palm to the left, field is still out of the page, thus induced current is down (thumb). So it flows from X to Y.

b. We basically already worked this out in the previous question - the induced current will create a force that opposes the applied force, thus the force is to the left.

7a. Exact same as 6a, however when we oppose the force by facing our palm to the left, the field is into the page, thus our fingers go into the page, thumb points up so current is from Y to X.

b. Force is still to the left as the external force is still to the right.

8. Clearly A, as the induced current always opposes the change.