# 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...

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.

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### 1 Answer

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:

dF=l*ds*B=T*dt, T=l*ds*B/dt=I*B*R

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