Electromagnetic Induction isn't a complex concept. Faraday, one of the principal founders of electricity and physics, discovered that if he moved a wire through an electric field- it produced a current. This is electromagnetic induction. The current direction can be found using the third left hand rule, which you already know.
When a wire moves in a magnetic field, a force acts on the charges in the wire. Work is done on the charges. Their potential energy is increased, thus the potential difference is increased. This is called inducing an EMF. EMF stands for electromotive force, but EMF isn't really force at all. EMF is measured in Volts, just like potential difference. The term EMF is misleading, but there is nothing you can do about it- it has been used since before electricity was fully understood.
To calculate EMF, you use a simple formula:
EMF = BLv
This should be easy for an experienced physicist like you to understand. EMF in volts equals the magnetic induction times the length of wire times the velocity of the wire.
We hope you still remember what vectors are. When a wire moves in a magnetic field, only the resolved velocity vector which is perpendicular to the field produces a current. You need to use only the perpendicular velocity, so be careful, sometimes questions can be confusing.
Faraday also invented the generator. Remember the electric motor? Well, the generator is the same. Exactly. Only instead of electricity turning the loop of wire, we ue a force to turn the loop, which produces electricity. Technically, if you spin a motor you are generating electricity.
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