A direct current I flows in a long straight conductor whose cross section has the form of a thin halr-ring of radius R. The same current flows in the opposite direction along a thin conductor located on the axis of the first conductor. Find the magnetic induction froce between the given conductors reduced to a unit of their length.

Answer

`F/l=(mu_0I^2)/(pi^2R)`

Explanation

Let us first hadn magnetic field at O due
to '1'.
`dB=(mu_0dI)/(2piR)`
where `dI=(IRd theta)/(piR)=I/pi d theta`
`implies dB=(mu_0)/(2piR) I/pi d theta`
Net field will be along ON:
`B=int_(-pi/2)^(pi/2)dBcos theta=int_(-pi/2)^(pi/2)(mu_0I)/(2pi^2R) cos theta d theta =(mu_0I)/(pi^2R)`
`F=BIl=(mu_0I^2)/(pi^2R)I implies F/l=(mu_0I^2)/(pi^2R)`