Consider the situation shown in . The wire PQ has mass m, resistance r and can slide on the smooth, horizontal parallel rails separted by a distance l. The resistance of the rails is negligible. A uniform magnetic field B exists in the rectangualr region and a resistance R connects the rails outsided the field region At t= 0, the wire PQ is puched towards right with a speed `v_0`. find (a) the current in the loop at an instant when the speed of the wire PQ is v, (b) the acceleration of the wire at this instatn, (c ) the velocity v as a function of x and (d) the maximum distance the wire will move.

Explanation

(a) When the speed is v `
`emf=B/v,`
`Resistance= r+R`
`:. Current = (Blv)/(r+R)V`
`(b) Force acting on the wire =i//B`
`=(BlvlB)/(R+r)=(B^2l^2v)/(R+r))`
` Acceleration on the wire`
``
`(c ) v=v_0+at=v_0-(B^2l^2v)/(R+r))t`
` [Force is opposite to velocity ]`
`v_0-(B^2l^2v)/(R+r))`
` (d) a=v(dv)/(dx)=(B^2l^2v)/(R+r))`
` dx= (dvm(R+r))/(B^2l^2)`
`x=(m(R+r))/(B^2l^2)`.