We are first keeping a focus on examples of Faraday's law where induced emf = -B dA/dt. This is when the wire loop or circuit is moving into or out of a region where there is a magnetic field.
1) The good news is that the math is always the same - the result is induced emf = -Blv.
2) Also, because the free, delocalized electrons of a moving conductor are actually moving, they feel a magnetic force F = qv x B...this is the force that starts the current in the wire loop!
3) Then, this induced current is in the external Bfield, and feels a force F = Il x B. This magnetic force on the wire loop will be opposite the velocity, acting like a magnetic brake.
Check out these videos:
Some good simulations that show applications of EM induction. Play with these, change parameters, and observe what the effects are of things like rate of change of flux, how the flux changes, the number of coils, DC versus AC currents, and the area of the coils.
http://phet.colorado.edu/en/simulation/generator Click on Run Now, and see the five different simulations that can be run, including generators and transformers and pick-up coils. Also keep Lenz's law in mind to see if Nature is trying to stop the magnetic flux from changing.
Also, this one is on Faraday's law:
http://phet.colorado.edu/en/simulation/faradays-law Click on Run Now, and move the magnet like in our labs to create an AC current. Pay attention to Lenz's law, and see if it makes sense with what you observe in the simulation.