A coil made of wire of copper, with wire's diameter d, traversed by a current I, is coaxial set into a magnetic field.
At what magnetic induction the coil is breaking?
The copper breaking stress is sigma=280MN/m^2 and radius of coil, R.
We'll consider a spiral element, which comprises a central angle dt. The electromagnetic force is acting on the element, dF=l*ds*B; also the stresses T, from the bottoms, are acting on the element. The resultant of both stresses is centripetal:
2*T*sin(dt/2)=2*T*(dt/2)=T*dt , ( (sindx)/dx=1)
The resultant is balancing the force dF, which is centrifugal:
On the other hand,T=sigma*S=sigma*(pi*d^2/4)
so that, B=T/(I*R)=(pi*d^2/4)*sigma/(I*R)
The usual magnetic fields are B<10T