A rod of mass `m`, length `l` and resistance `R` is sliding down on a smooth inclined parallel rails with a cinstant velocity `v`. If a uniform horizontal magnetic field `B` exists, then find thevalue of `B`.

Explanation

The emf induced in the rod,
`E = (B sin theta)lv`
`= Blv sin theta`
The current in the circuit `I = (E)/(R ) =(Blv sin theta)/(R )`
Magnetic force acting on the sliding rod, `F_(mag) = IlB`
`F_(mag) = ((Blv sin theta)/(R ))lB`
`=(B^(2)l^(2)v sin theta)/(R )`
If the rod is sliding with constant velocity,
`F_(mag)sin theta = mg sin theta`
`rarr` `=(B^(2)l^(2)v sin^(2) theta)/(R ) = mg sin theta`
`rarr` `B = sqrt((mgR)/(l^(2)vsin theta))`