A wire ab of length l, mass m and resistance R slides on a smooth, thick pair of metallic rails joined at the bottom as shown in the figure . The plane of the the rails makes an angle `theta` with the horizontal. A vertical magnetic field B exists in the region. if the wire slides on the rails at a constant speed v, show that `B = sqrt (mg R sin theta)/ sqrt (vl^2 cos^2theta)`.

Explanation

Since i=(Bccl cos theta xxv cos theta)/R`
`=(Blv)/® cos^2 theta`
`F=i//B =(blv cos^2 thetaxxlb)/R`
`Now F=mg sin theta`
`[ Force due to gravity which pulls downwards ]`
`Now , (B^2l^2v cos ^2 theta)/r= mg sin theta`
`B=sqrt((R mg sin theta)/(l^2v cos^2 theta))