and thank you in advance for taking the time to read my question. To give an idea of my working level, I'm a 21 year old computer science student entering my senior year at college. It's been a few years since my Electricity/Magnetism course, and i'm a bit rusty on the Lorentz Force.
I wanted to create a sort of "Human Powered Generator", ie. something as simple as a stationary bicycle turning a generator as I peddle. Now I know the "right hand rule", and can quite easily make a motor/generator with some wire and magnets. My question is about voltage/current. I was never clear on the effects of the strength of the magnet and its importance in the amount of potential power generated. In other words,
1.) If i'm turning a generator at a constant rate and it is lightning a bulb, if I magically replaced the magnets with ones twice as strong, what would happen? I'm assuming it gets twice as hard to turn, but outputs potentially twice as much power.
In addition, I was never clear on the relationship between voltage and current in the lorentz force.
2.) While turning a generator at constant speed S with magnets of strength B and # of wire coils C, how much voltage/current is created? I know there are many variables involved here, perhaps such as the width of the rod the coils are wrapped around, thickness of coils, etc.
Finally,
3.) If trying to charge a battery of V volts and A ampre-hours, what measures should I take to ensure safe delivery of energy to the battery? In other words, if I peddle the generator very rapidly, I expect lots of either current/voltage/both. I assume I need a voltage regulator of sorts, and I'm not sure if the current matters (I think its just how "much" energy there is, whereas voltage is the "pressure" or "strength" of the energy).
I appologize if any assumptions I made are incorrect, i'm just going off of old knowledge. I tried wikipedia, but its all symbolic and I cant find a hard example (As in, I dont know how to find magnetic strength of a magnet, always denoted as B in the equation). Thanks to anyone who can answer any/all 3 of my questions!
-John
Best Answer
First a few lines of basics. If you put a loop into the magnetic field and this loop turns within it, the magnetic flux through loop shall change according to the formula
$$\Phi_B = \vec{B} \cdot \vec{A} = B A \cos\phi = B A \cos\omega t,$$
where $\vec{B}$ is magnetic field strength, $\vec{A}$ is area of the loop and $\phi$ is angle between $\vec{A}$ (perpendicular to loop) and $\vec{B}$, while $\omega$ is angular velocity of the rotation of the loop.
If you use coil with $N$ loops, then induced voltage on the coil shall be
$$\mathcal{E} = N \frac{\text{d}\Phi_B}{\text{d}t} = - N B A \omega \sin\omega t.$$
Therefore, yes, if you use twice larger magnetic field, you get twice larger voltage.
However, twice larger magnetic field does not necessarily mean it is twice as hard to turn. For example, if you have no electric load on the generator, there is practically no current in the coil and there is practically no Lorentz force! However, if you have completely ohmic load, voltage twice larger means current twice larger and yes it becomes twice as hard to turn.
In practice, you should also consider the internal friction of the generator. So even if there is no load, some muscular power will be required in order to overcome friction. When you increase the electrical load, required power in order to turn generator increases.
Of course, it is difficult to keep rotation constant, which means that with larger angular velocity $\omega$ voltage increases. To keep generator's output voltage constant, you need some electronic circuit, of which the simplest possible includes zener diode.