Firstly, consider a magnet within a solenoid. As it moves from one side to the other, it induces an e.m.f.
If the solenoid forms part of a closed circuit then a small alternating current will also be produced:
This is assuming that the magnet is moving with constant acceleration/ deceleration. Hmm, constant acceleration…
Now imagine a mass held between two springs. It is in the perfect conditions where there is negligible air resistance or friction. The mass is displaced to one side so that one spring is extended, the other compressed:
The magnet moves with a constantly changing velocity to –x0 (remember that this is a perfect system), and then back to x0 and… I’m sure you can imagine where this is going…
I haven’t read or seen anything like this before so I’ve been working on a mathematical representation. So now for the equations …
Lenz and Faraday told us this:
and another scientist (unknown to me) told us this:
Now we can combine them. But first, consider what dt and t actually mean. In simple harmonic motion t is for the equivalent complete circle or basically going back to the start-
However, in electromagnetic induction, the magnet is only considered moving from one side to the other. Therefore, the relationship is such:
If you’re qualified, I’d appreciate it if you checked for mistakes here on…
Bear with me, the d’s will be explained…
Now we can equate the t and 2dt
Now to rearrange in terms of E.
Okay, here’s the thing about the dΦ/ dt. A basic textbook example would say something like:
“In 20 seconds the magnetic flux on a coil of wire dropped from a value of 20Wb to 0Wb. There were 300 coils of wire, what is the induced e.m.f?”
The d’s are there because the e.m.f is induced due to a change in magnetic flux with time. In the equation, the lone dΦ needs to be remembered as the change in magnetic flux for the movement of the magnet from x0 to –x0 and from –x0 to x0.
The equation is homogeneous with respect to units, so I can’t have made any serious errors in my working. You may well want to check that yourself. Anyway, that’s my explanation done; time to consider why it could be useful…
Where, when, what?
Well, if you’ve ever had a toy or contraption with a spring on it, you’ll know it doesn’t take a lot of movement to make it shake about in a crazy kind of way. So, imagine one of the springy inductors (it’s the best name I can think of) in a vehicle, or attached to your belt, or maybe even sitting on top of the washing machine!? The magnet would be shaking about in the solenoid, inducing e.m.f, harnessing the kinetic energy of something else. If it’s in a circuit, then the energy could be stored in a battery. Who knows, if there were enough of them, maybe it could power a car… Although the car would probably weigh tonnes.
Anyway, there is a limit to how much I can do… hopefully you people out there can get in touch with comments and maybe a little advice. I have been thinking about this for a few years, so if you want to research this further, I’ll be pretty annoyed if you don’t get in touch with me first. While imagination is free, patents are not! Oh, and tell your friends, relatives, teachers, colleagues, employees, bosses, (or just random people you meet!) about this site- I’d like as many people as possible to provide an opinion!
Timeline
October 2002 - First considered using the kinetic energy of a vehicle as its power source.
March 2004 - Thought up the magnet-in-springs generator. Although I hadn’t yet heard of electromagnetic induction.
April 2006 - Managed to create a sensible equation! (Well I think I did anyway…)
March 2007 - Made this blog!
