A coil carrying a current `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 `0*1mm`, radius of turns is equal to `30mm`. At what value of the induction of the external magnetic field can the coil winding be ruptured? Breaking stress is `3*1xx10^8Nm^-2`.

Explanation

Each element of length `dl` expression a force `Bi dl`. This causes a tesnion `T` in the wire.
For equilibriium,
`T d alpha = BI dl`,
where `d alpha` is the angle subtended by the element by the element at the centre,
Then, `T = BI (dI)/(d alpha) = BI R`
The wire expreiences a stress
`(BIR)/(pi d^(2)//4)`
This must equals the breaking stress `sigma_(m)` for rupture. Thus,
`B_(max) = (pi d^(2) sigma_(m))/(4 IR)`