Question

A coil carrying a current $I=10mA$ is placed in a uniform magnetic field so that its axis coincides with the field direction. The single-layer winding of the coil is made of copper wire with diameter $d=0.10mm$, radius of turns is equal to $R=30mm$. At what value of the induction of the external magnetic field can the coil winding be ruptured?

Answer 1

Each element of length $dl$ experiences a force $BIdl$. This causes a tension $T$ in the wire. For equilibrium,
$Td\alpha =BIdl$,
where $d\alpha$ is the angle subtended by the element at the centre.
Then, $T=BI\frac{dl}{d\alpha }=BIR$
The wire experiences a stress
$\frac{BIR}{\frac{\pi d^2}{4}}$
This must equals the breaking stress ${\sigma }_m$ for rupture. Thus,
$B_{max}=\frac{\pi d^2{\sigma }_m}{4IR}=8kT$