# Correct formula for induced voltage with a stationary coil?

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1. Sep 23, 2016

### NickS1

I'm making an AC generator with a stationary coil and rotating magnets. What would be the correct formula to find induced voltage at a certain rotation speed (along with the units)? All sources I've found are either non-applicable or do not explain what units to use.

Thank you for the help.

2. Sep 24, 2016

### Simon Bridge

The one that tells you the rate that the magnetic flux enclosed by the coil changes.
Stationary coil and rotating permanent magnets is a complicated problem ... you can probably get approximate solutions for specific geometries so what kind of generator are you thinking of building?

3. Sep 28, 2016

### NickS1

A 4.5" tube that's 1/2" thick, with 1,000 wraps of 30 gauge magnet wire around that. Two neodymium disk magnets spin inside of the tube (magnetized on the face, less than 2/5" from the center of the magnet to the inside of the tube.

4. Sep 29, 2016

### Simon Bridge

Not enough information ...

5. Sep 30, 2016

### NickS1

What other information is needed?

Edit:
I know of the formula ε=NABω sin ωt , but I do not know what unit B is, other than that it is the B field. This equation doesn't seem to make sense in the context of a stationary coil, however.

I also know the formula ε=-N(ΔΦBt) , where Φ≡BA cos θ
B calls for a uniform magnetic field, which doesn't work in the context of a rotating field. (I also do not know θ)

Last edited: Sep 30, 2016
6. Oct 1, 2016

### Simon Bridge

You need more geometry - for instance, how are the magnets turning in the coil?How strong are they? What are their dimensions? etc.
The key to the equation is the model you use for the geometry of the magnetic field of the permanent magnets.
The equation will need to be derived too - unless your design corresponds to a very common one.

7. Oct 1, 2016

### NickS1

1" diameter 1/4" thick N52 grade neodymium magnets, with a surface field of 3309 Gauss. They are both attached 1.68" from the very center of the coil. How would I go about deriving such a formula?

8. Oct 1, 2016

### Simon Bridge

By making a careful mathematical description of the $\vec B(\vec r, t)$ field produced by the magnets and applying Maxwell's equations.
You'll probably model the magnets as dipoles - and you still have not got enough geometry for them or how they are set to rotate.

ie. Is this a toroidal coil and the magnets slide round and round the inside?

9. Oct 3, 2016

### NickS1

It is not a toroidal coil, the wire is wrapped on like fishing line is wrapped on. If I am interpreting you correctly, the magnets do slide around like you describe. They rotate on a pivot that is perpendicular to the plane of the "circle:" the wire is wrapped on.

10. Oct 3, 2016

### Staff: Mentor

@NickS1 I think the better answer is that there is no simple formula. The voltage of a generator also depends on the load applied.

Your time might be better spent building and experimenting rather than calculating.

11. Oct 3, 2016

### Simon Bridge

Then you can get a back-of envelope estimate because you know the B field reverses every half turn.
The 1st order approx will be a sine wave with the freqeuncy as the turn rate and the amplitude determined from the estimate.
This sort of thing is usually good enough to start building from, then you can refine the design from experimentation.