I will look into the math a bit later, but this remind me of a calculation I was doing last year. I was trying to find the force for a rail gun, and I noticed that assuming ideal wires doesn't work as the force does go to infinity. The moment you deal with the wire's geometry and resistance, you see that as you make the wire thinner, the current drops proportional to the area, and the force drops proportional to the square of the current, but increases due to the reduced corner thickness. When all of the dust settles, you see that making the wire thinner, eventually leads to making the force less. You can argue to use super conducting wire, but in reality, the sharp angles will fail because of the high currents and magnetic stresses.
I will look into the math a bit later, but this remind me of a calculation I was doing last year. I was trying to find the force for a rail gun, and I noticed that assuming ideal wires doesn't work as the force does go to infinity. The moment you deal with the wire's geometry and resistance, you see that as you make the wire thinner, the current drops proportional to the area, and the force drops proportional to the square of the current, but increases due to the reduced corner thickness. When all of the dust settles, you see that making the wire thinner, eventually leads to making the force less. You can argue to use super conducting wire, but in reality, the sharp angles will fail because of the high currents and magnetic stresses.
ReplyDeleteIt is for an ideal current of zero thickness that the force is infinite.
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