The long, horizontal pair of rails shown in the figure is connected using resistance R. The distance between the rails is l, the electrical resistance of the rails is negligible. A conducting wire of mass m and length l can slide without friction on the pair of rails, in a vertical, homogeneous magnetic field of induction B.
A force of magnitude `F_(0)` is exerted for sufficiently long time onto the conducting wire, so that the speed of the wire becomes nearly constant. The force `F_(0)` is now removed at a certain point P What distance (inm) does the conducting wire cover on rails from point P before stopping? (Given `F_(0)=20N, m=1.6 gm, R= 0.01 Omega l=19 cm, B=0.1 T)`

Answer

`0320.00`

Explanation

For constant velocity
`a=0`
`F_(0)=F_(m)`
`=ilB=((varepsilon)/R) lB = ((Blv_(0))/R)lB`
`v_(0)=(F_(0)R)/(B^(2)l^(2))` velocity at point 'P'
Now retardation `a=F_(m)/m=(ilB)/m`
`a = (B^(2)l^(2))/(mR)v`
Rightarrow `-v(dv)/(ds) = (B^(2)l^(2))/(mR) v`
`or -underset(v0)overset0intdv=(B^(2)l^(2))/(mR)underset0oversets intds`
`or v_(0)=(B^(2)l^(2))/(mR)s`
`or s=(mRv_(0))/(B^(2)l^(2))=(F_(0)mR^(2))/(B^(4)l^(4))=320 m`