Solenoid, Magnet, Lenz & Faraday, Light Bulb

Illuminitwit

1. The problem statement, all variables and given/known data
"A light bulb is connected to a coil of wire. If a magnet is passed back and forth through the coil the bulb will light up. Why?"


2. Relevant equations
The Lenz Law isn't really an equation, but it states that: "The magnetic field of the induced current is in a direction to produce a field that opposes the charge causing it."
Faraday's Law: emf = -N(∆ΦM / ∆t)
emf is electromotive force,
N is number of loops in the circuit,
∆ΦM is the magnetic field strength,
∆t is the time


3. The attempt at a solution
Here's what I've written so far, but I think it sounds a little strange because I'm not sure I used the concepts and terms correctly:

"The solenoid connected to the light bulb has the ability to act like a magnet if a current is sent through it. When a magnet approaches the solenoid, according to Lenz's law, the magnetic field creates an induced current in the solenoid that produces a magnetic field that opposes the magnetic charge causing it. If the magnet passes back and forth through the coil and continues moving, it creates an alternating current that lights up the bulb."

If you could please read it for me and point out any errors in use of Physics concepts or errors in understanding that would be better explained another way, I'd greatly appreciate it. Thanks! :)