Does voltage limit the magnetic force of a coil? My question I had is whether it is strictly current that creates the magnetic force in the coil or if voltage is also relevant? The reason for this question is because I figure if it is just current could I not take a low voltage battery but use an extremely low resistance wire in order to create a large current? I assume this is not possible or the many videos Ive seen wouldn’t use the 300 volt super capacitors but I’m curious why it wouldn’t work if it indeed does not. Thank you in advance for any insight you can provide me in how a coil gun really works beyond general concepts. I am currently trying to build a coil gun for a school project in an engineering program and am facing certain resource constraints put on me by the professor. I have looked at many different coil gun builds from other people but they tend to use super capacitors or 20 volt batteries among other things in order to achieve the current required to move the projectile.
Also if you wanted to help me with any other insights on how to design my coil gun I only have access to .001f capacitors, a 5 volt battery, a list of some circuitry tools (resistors, diodes, MOSFETs…), and a $50 budget(some of this must be allocated to buying the actual coil). I basically have freedom to design the coil gun however I wish other than those constraints. I am wondering if it is possible to shoot even a small projectile (5 grams or so) with these constraints. If so what would be the best way to do it, charge many of the capacitors, use the 5 volt battery with circuit techniques? I’m in first year engineering so I’m only now learning about electric circuits and magnetism. I tried looking at resources online but have found conflicting data. I have also spoken to a few physics profs as well as one electronics prof(for the circuit side of this project) and all of them said they they didn’t have enough knowledge on the specifics of how coil guns worked and the different challenges involved so ultimately weren’t able to help me more than sending me in the right direction. Any suggestion are appreciated.
 A: 
could I not take a low voltage battery but use an extremely low resistance wire in order to create a large current?

Absolutely. Yes. Consider a typical MRI machine with a superconducting magnet. When the machine is in use, the current in the coil typically is in the hundreds of Amperes, but the voltage is zero.

I assume this is not possible or the many videos Ive seen wouldn’t use the 300 volt super capacitors

Your "coil gun" needs to create a strong, but brief magnetic pulse.  That superconducting MRI magnet doesn't need any voltage to keep the current flowing but it needs voltage to change the current. The current in an ideal inductor changes at a rate proportional to the applied voltage. If you want the current to quickly "ramp up," then you must supply a high voltage.
A: Voltage and current are not parameters you control independently. For a given coil, the current will be proportional to the voltage, so increasing the voltage will increase the current. It is ultimately the current (along with the coil geometry, e.g. the number of turns) that determines the magnetic field inside the coil. However, you will find that it's not easy to just use "extremely low resistance" wire to get enough current. You are basically limited by the resistivity of copper, which is by no means negligible for purposes of designing such coils. You can use lower gauge (thicker) wire, but this means you can't wind the coil as tightly as you can with a thinner wire, i.e. you will get fewer turns of wire per unit cross section area, which reduces the magnetic field for a given current.
Before blindly ordering parts and choosing components willy-nilly, especially since you are on a budget, I advise you to do some math to see the tradeoffs involved and how the voltage, capacitance, coil geometry, resistance and inductance impact your magnetic field amplitude and duration (and perhaps the spatial variation). At the very least you can run some simple circuit simulations (e.g. with LTspice) to see what kind of currents you can expect, and estimate the corresponding magnetic field using a simplified coil geometry, or using free calculators available online. For example, a higher capacitance may not necessarily increase the peak magnetic field (or force), but it will give you a magnetic field pulse that lasts longer, imparting more impulse on the projectile (assuming it is traveling sufficiently slowly).
A: The voltage plays no role other than to generate the current. The problems with very high currents are to maintain the mechanical stability of the conductor and to cool it.
