Coil, 110 GA, r = 70m. How much tension force is generated?

[nehorlavazapal]

Homework Statement

I need to generate a field of B = 10 T at the center of a magnetic loop (coil). The coil should have r = 70 m. The coil material itself should be a cable of r = 0.2 m. The question, how much mechanical stress is applied throughout the loop? I'm trying to figure out, if such a material (coil) could be made.

Homework Equations

Not needed, as the magnetic field equations are widely known among the visitors of the forum. On the other hand, I don't know the relevant equations related to the loop stress (tension forces)

The Attempt at a Solution

The current flowing through the loop must be 110 GA.

Force per meter F/L between wires separated by 1 meter from F/L = mu_0I^2/(2pid):
= 2.42×10^15 N (Newtons). But I have no idea what to do in the case of a loop (is it lower by factor of 70^2 ? or 140^2?). Is it 1,23*10^11 N or 5*10^11 N? Please help.

 

[mfb]

If you don't care about small prefactors (like 2, or 1/2), I think assuming a wire at 70m distance will give the right order of magnitude. Note that you have to convert "force per meter" to "tension in the cable" afterwards (the second value will be much larger). A proper analysis would involve integrals over the loop.
Anyway, a support structure can handle this.

I don't think the application for this coil is properly designed.

 

[nehorlavazapal]

I can't afford a support structure, it's antimatter drive designed to intercept only a fraction of the hard gammas produced in anihilation. It is not a viable option.

Some new physics is needed to take care of the gammas, the antimatter drive as currently pressented is dead. It needs to produce terrawatts of energy just to produce veery slow accelerations and those TWs of gammas just mlet away and erode the engine during the boost years. If you increase the mass you also push the accel. time to centuries. The loop would allow for 1/4 c in 50 years. However, it breaks.