Calculating induced power in coil

1. Jul 10, 2006

Jdo300

Hi,

I'm working on making a coil and I was wondering if there are some nifty equations out there to predict how much power the coils can make under a changing magnetic field of X gauss. I am going to be using 1 inch of a 3/8" x 2.25" bolt to wind my coil onto and I will be exposing it to a 2000 gauss field from a 0.5" x 0.5" neo magnet that is placed on the end of the coil.

I used a gauss meter to measure the amount of flux coming out of the side of the bolt where I will be wrapping the wire, and it is about 320 gauss. If I could mechanically vary this field strength on the coil by ±5% (304 - 336 gauss) at frequency X, how would I determine the power output? I am planning on using 20 gauge magnet wire for the coil, which will be 1" tall, and 1.5" in diameter.

Any help/pointers would be great

2. Jul 11, 2006

Andrew Mason

The induced voltage depends on the diameter (area) of the coil and the number of turns of the coil. The power is determined as well by the resistance of the coil. Faraday's law will give you the induced emf in the coil:

$$V_{induced} = \frac{d\phi}{dt} = NA\frac{dB}{dt}$$

That is the potential energy per unit charge in the coil. If the coil is connected to a load, there will be energy consumed. The current will be I = V/R. The power is

$$P = VI = V^2/R = \frac{N^2A^2}{R}\left(\frac{dB}{dt}\right)^2$$

AM

Last edited: Jul 11, 2006
3. Jul 11, 2006

Jdo300

Hi, what units are those variables in? is B in gauss or Tesla?

Thanks,
Jason O

4. Jul 11, 2006

Andrew Mason

All SI units. One Tesla = 10,000 Gauss.

AM

5. Jul 11, 2006

Jdo300

Hi,

Thanks for the info. How do I account for the frequency at which the magnetic field changes? If I were to assume that the function of B was sinusoidal, then how do I account for the amount of voltage at frequency X? It gets even a bit weirder in my case because the field is not varying from positive to negative but using a function which I made based on the graph from the simulator. Another thing I'm wondering is if the field I should be calculating is the field that is coming out of the sides of the bolt into the coil, or the field that is coming directly from the face of the magnet into the bolt? Once I can get this straightened out, I already know the information about the wire. I calculated that for the dimensions of my coil, I would have about 320 turns of 20 gauge wire, which according to the wire chart is 0.093 Ohms (I changed the diameter of the coil to 1.25 in by the way).

Thanks,
Jason O