Cool physics equations

[Sapper]

I was walking around my campus the other day and recalled a leacture on electromagnetic field physics. I got to thinking .. as a conductor is moved through a magnetic field (such as the one that the earth produces) an electric potential is created.

The voltage of the induced potential is as follows:

EMF = v* l * B * sin(theta)

EMF = voltage (electromotive force)
v = velocity
l = length of conducting rod
B = magnitude of magnetic field
theta = the angle between the velocity vector and the magnetic field vector

So i thought to myself, how fast would I have to run if I wanted to power my walkman (which runs on 3.0V) if my arm span were 1.8m - assuming of course I were to conduct the electricity from finger tips to my walkman.

Ok, I will now introduce physics land - a place where you can ignore variables to simplify these thought experiments. We will ignore all confounding variables such as resistance, drag, etc.

so we re-arrange the above equation and obtain the following:

v = EMF / l * B * sin(theta)

Ok, how strong is Earth's magnetic field? Well, it is equal to approximately 5.0e-5 T. My velocity will be at 90 degrees to the magnetic field of Earth.

What must my velocity be to power the walkman?

Answter: 33'333 m/s or 33.3 km per second !!

[Paq]

answer: pretty f'ing fast

very cool equation, though

[Peetster]

While you've created the potential voltage, you are going to fall short on amperage. Despite your velocity, I think you're going to miss power requirements by an order of magnitude.

[Sapper]

As I noted in the thought experiment, this is in physics land (a place where we can ignore confounding variables to keep these demos simple). I have chosen to ignore Ohm's law, etc. for the purposes of simplicity - I could add in total circuit resistance, etc but will avoid it for now.

If anybody wants to add to this thought experiment, find the current required to run the walkman. Be sure to "set" a resistance value.

More importantly though, how much power is required - this can tell you what the efficiency of running across the earth's surface to power a walkman is in comparison to a battery. This would be a ratio of "Power".