## Friday, April 18, 2014

### How to do the "Hardest Induction Problem Ever!"

I've given a problem to my students in E&M as a challenge problem - I call it the "hardest problem ever."  It is a Faraday's law problem, where we have a circuit made of a bar sliding down a frictionless hill inside a constant magnetic field.  This is the type of problem where the emf = -B dA/dt.

First, recognize that any problem where the area changes has the same answer for the emf:  emf = Blv.  This will be the case once again, as shown in the video.  The challenging part of this is that, on a hill, there is a gravity component.  There is also, in every type of problem like this where the area changes, a magnetic braking force (this tries to slow down the change in flux, and fits in with Lenz's law).  If the magnetic braking force is the only force, it will slow the bar exponentially, like air friction on a hockey puck.  But here, when there is a constant force trying to speed it up in addition to the magnetic braking force, we have a behavior like a sky diver - a terminal speed is reached!

Check out the details and see if it makes any sense.