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Hello! So I'm hopelessly lost on a few concepts here, and I'm putting myself at the mercy of the giant super-human brain they call the 'web' for answers.

I'm trying to make a linear solenoid electromagnet. Specifically, I want to shoot a nail through it. Like a railgun. Just for kicks. But I also want to shoot that nail as efficiently as super-humanly possible.

I've been experimenting with several different variables, and trying to maximize the force on the nail. From what I've deduced, force is proportional to the strength of magnetic field that my coil induces. (Assumption #1).

So if I can increase that magnetic field at the center of the coil (a quantity often called "B"), I can more effectively shoot the nail. I have come to understand that, for a solenoid, according to Amperes Law or somesuch,

B = [LATEX]\frac{\mu I}{4 \pi} \oint \frac{\vec{dl}\times \hat{r}}{r^{2}}[/LATEX]

With all the vectors, that gets messy, but it can really be simplified if you look at just one turn of wire, and solve for the magnetic field right there in the center of it, pointing only in the axial direction. My confusion isn't with the math so much as with the concept of it.

Here's where I'm getting stuck:

In the above equation, it would appear that more current "I" means more magnetism "B". And, the smaller the radius of the solenoid "r", the more magnetism also. I would assume that the more times you compound the effect by adding more turns of wire, you'd also increase the magnetism. HOWEVER, by increasing the turns of wire, would you not also increase the resistance in the wire? For a given input voltage "V", the current really depends on the length and area of the wire. So, in a gross yet practical over-simplification of the "B" equation,

B = (some constants) * I * N / r

I = (some constant) * V * Area-of-wire / length-of-wire

where N, the number of turns, is *linearly proportional* to length-of-wire. Notice how I also divided by length-of-wire just there. SO, why on earth does the number of turns of wire matter at all? Wouldn't the positive effect of more turns be canceled out by the negative effect of more resistance? It would seem, to the casual observer, that the only true way to improve a solenoid is to increase the voltage and wire-size, and decrease the radius of the loops. But a century of industry would beg to differ. What am I missing!?

I'm trying to make a linear solenoid electromagnet. Specifically, I want to shoot a nail through it. Like a railgun. Just for kicks. But I also want to shoot that nail as efficiently as super-humanly possible.

I've been experimenting with several different variables, and trying to maximize the force on the nail. From what I've deduced, force is proportional to the strength of magnetic field that my coil induces. (Assumption #1).

So if I can increase that magnetic field at the center of the coil (a quantity often called "B"), I can more effectively shoot the nail. I have come to understand that, for a solenoid, according to Amperes Law or somesuch,

B = [LATEX]\frac{\mu I}{4 \pi} \oint \frac{\vec{dl}\times \hat{r}}{r^{2}}[/LATEX]

With all the vectors, that gets messy, but it can really be simplified if you look at just one turn of wire, and solve for the magnetic field right there in the center of it, pointing only in the axial direction. My confusion isn't with the math so much as with the concept of it.

Here's where I'm getting stuck:

In the above equation, it would appear that more current "I" means more magnetism "B". And, the smaller the radius of the solenoid "r", the more magnetism also. I would assume that the more times you compound the effect by adding more turns of wire, you'd also increase the magnetism. HOWEVER, by increasing the turns of wire, would you not also increase the resistance in the wire? For a given input voltage "V", the current really depends on the length and area of the wire. So, in a gross yet practical over-simplification of the "B" equation,

B = (some constants) * I * N / r

I = (some constant) * V * Area-of-wire / length-of-wire

where N, the number of turns, is *linearly proportional* to length-of-wire. Notice how I also divided by length-of-wire just there. SO, why on earth does the number of turns of wire matter at all? Wouldn't the positive effect of more turns be canceled out by the negative effect of more resistance? It would seem, to the casual observer, that the only true way to improve a solenoid is to increase the voltage and wire-size, and decrease the radius of the loops. But a century of industry would beg to differ. What am I missing!?

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