Current induced by magnet: maximize change in flux wrt time?

[Battlemage!]

I'm messing around with Faraday's Law of Induction, and I will be using two magnets attached either side to a small bar inside two coils of copper wire, which I spin to induce a current. The design is basically this:
http://amasci.com/amateur/coilgen.html

My question is, what shape for the magnet should I go with to maximize the current, assuming the loops of wire and rate of rotation of the magnets are constant?

Should I go with long, skinny magnets? Short, fat ones? I know I need the poles of my magnets to change constantly in order to induce the current, and I've found that squarish magnets work a lot better than disk ones, at least by the tests I've done. At this point my available options are magnets with these characteristics (the strength is not constant here, neither is the geometry):

1. Grade N45 bar magnet with dimensions of 4 inches by 1/2 inches by 1/2 inches

2. Grade N52 block magnet with dimensions of 2 inches by 1/2 inches by 1/4 inches.​

I will build the device so the coils are as close as possible to the magnets. Assume the radius of the coils goes out 1 inch past the long side of the magnet (so in the first option the radius is 5 inches, the second it is 3 inches), and that the two coils of wire are each one inch to the side of the magnets. Which do you think will provide more current, assuming I spin both types at the same rate? Thanks.

 

[Hesch]

First of all: Faraday does not say, that a current is induced, but a voltage, meaning that if the coils are not connected to a load, no current will flow, but there will be a voltage, but you may consult Ohms law what matters the current.

As I remember (?) you must maximize the magnetic energy in the airgap between the coils and magnetic circuit. This energy:

E_magn = ½*B*H [ J/m³]

So you have to calculate the magnitizing characteristic of your magnetic circuit and find the point where B*H has a maximum. I think its important that the bar is made of steel ( high permeability ).

 

[Battlemage!]

Thanks for that. If H is the strength of the field, and that strength decreases with the square of the distance, I'm thinking I need to choose the shape that enables the smallest radius from the wire to the magnet, which in this case is the short fat one. Do you think that will help?Anyway, if resistance were unity wouldn't that mean V = I times one (ohm)? Either way, I can detect both current and voltage with my multimeter with the first one of these I built. It's just embaracingly weak in both cases. Thanks for the insight and anything else you want to add.

 

[Hesch]

Thanks for that. If H is the strength of the field, and that strength decreases with the square of the distance, I'm thinking I need to choose the shape that enables the smallest radius from the wire to the magnet, which in this case is the short fat one. Do you think that will help?Anyway, if resistance were unity wouldn't that mean V = I times one (ohm)? Either way, I can detect both current and voltage with my multimeter with the first one of these I built. It's just embaracingly weak in both cases. Thanks for the insight and anything else you want to add.

1) How do you know, that the H-field will decrease with the square of the distance? I agree that it will decrease, but the decreasing-function depends on the magnetic circuit as a whole. For example if you place an iron-frame outside the coils and thereby increase the (mean) permeability of the total magnetic circuit, you will increase the intensity of the B-field, and therefore the energy density in the airgap. ( You may call this frame the stator of a generator/motor ).

Notice that the unit for magnetic energy is [ J/m³] so when you decrease the distance, you will also descrease the volume in which the magnetic energy is included, and thereby decreasing the magnetic energy.

So all in all it's very difficult to calculate magnetic fields and energy, and designers of motors/generators use computerprograms (CAD) to optimize eg. a motor.
( Sorry for my answer. It was not to much help ).

2) I would rather formulate it: I = U / R, as current is "induced" by voltage, ( not in reverse order here ). Your generator is more like a constant voltage source, than a constant current source.

 

[Battlemage!]

Lol I just assumed (foolishly) that it was basically the same as Coloumb's law. I suppose I should study some physics before trying physics experiments.

(seems I lost the rest of my post here).

Anyway, let me see if I understand this.

On one hand, wouldn't decreasing the distance increase the field lines per unit volume, thereby increasing magnetic flux, and if the magnet is moving, wouldn't that increase the time derivative of magnetic flux, thereby increasing the induced emf?

But on the other hand, you're saying that decreasing the distance would decrease the volume that includes the magnetic energy? And that wouldn't increase the energy density? Like with a field around a sphere, smaller radius means closer together field lines? Or does it not work like that?

Anyway, I will have my magnets tomorrow, and I will get the chance to test just how the radius affects the induced voltage. I wonder if there is an inflection point somewhere along the radius distance from the magnet to the coil of wires. I suppose I can also try several different orientations of the magnets with respect to the coils. Will be a lot of fun.

Thanks again for your response and any more insight you have.

 

[Hesch]

On one hand, wouldn't decreasing the distance increase the field lines per unit volume, thereby increasing magnetic flux, and if the magnet is moving, wouldn't that increase the time derivative of magnetic flux, thereby increasing the induced emf?

But on the other hand, you're saying that decreasing the distance would decrease the volume that includes the magnetic energy? And that wouldn't increase the energy density? Like with a field around a sphere, smaller radius means closer together field lines? Or does it not work like that?

Yes, you have understood it correctly.

If you have a "normal" motor with an iron stator (iron frame) and an airgap, the B-field will be the same in the airgap as in the iron on both sides of the airgap, but the H-field will not. As the relative permeability is about 1000 in iron, the H-field will be 1000 times higher in the airgap than in the iron. Therefore a higher energy density in the airgap of a normal motor. But if you increase the thickness of the airgap (increasing the volume of the airgap) too much, the airgap will be dominant in the magnetic circuit as a whole, and the strength of the H-field will decrease. And if you decrease the thickness of the airgap too much, the volume of the airgap will disappear, so there is an optimum somewhere in between.

It's a very important point, because if you ask where the torque of a motor/generator is created? the answer is: In the airgap. Why are two magnets attracted to one another? Because there is an airgap between them. Mother nature will always try to eliminate a (high-density) magnetic energy. In case of the two magnets by let them close up, so that airgap is substituted by iron/steel, in where the magnetic energy has lower density.

In the same way, mother nature will try to eliminate potential energy: If you hold a ball in some height and let it go, it will drop, converting potential energy to kinetic energy.

 

[Battlemage!]

Yes that makes a lot of sense Hesch. The natural state is equilibrium, just like with gravitational potential energy. So you want to take advantage of that to maximize the utility of the device without fully giving into nature, it seems. Thanks again.