A ring of radius `r_0 = 20` cm made of a very thin wire cariries a current of I= 10 A. The tensile strength of the wire is equal to `T_s = 1.5`N. The ring is placed in a magnetic field, which is perpendicular to the plane of the ring so that the forces tend to break the ring. The required magnetic field to break the ring would be --------- T.

Answer

`2.5`

Explanation

`dl=r_0dtheta`
For the equilibrium of a small part of semicircular arc subtending an angle of `dtheta` at the centre,
Mechanical force = magnetic force
`implies2 Tsin((d theta)/2)=BIdl`
`=BI(r_0d theta)`
`implies 2T (d theta)/2=BI(r_0d theta) ...`
`.[overset( :. for theta to 0)(sin theta to theta)]`
`implies B=T/(Ir_0)=(1.5)/(3 xx 0.20)=2.5T`