A square loop of edge a has `N` turns and a total resistance `R` . The loop moves with constant velocity `v` through a region of constant magnetic field `B` . The loop enters in magnetic field at `t=0`. Discuss the vartion of (a) Flux passing through the loop (b) the induced emf and (c) the external force acting on the loop a function of position of the loop in the field.

Explanation

(a) `0ltxlta`
`phi+Nbax` , `phipropx`
`e=-(dphi)/(dt)=-Nba(dx)/(dt)=-Nbav`
Induced current, `I=(e)/(R)=-(Nbav)/(R)`
Flux is inceasing the direction of induced current which is anticlockwise.
Mafnetic force on the loop=magnetic force on side `BC` :
`F_(m)=NBIa=(NB^(2)a^(2)v)/(R)` , towards left
(b) `altxlt4a` :
`phi=NBa.a=NBa^(2)`
`e=0` , `I=0` , F_(m)=0`
(c) `4altxlt5a` :
`phi=NBa[a-(x-4a)]=-NBa(5a-x)`
`e=-(phi)/(dt)=NBa(dx)/(dt)=NBav`
`I=(e)/(R)=(NBav)/(R)` , Flux is decreasing, current will be clockwise.
Magnetic force on the loop=magnetic force on the side `AD` :
`f_(m)=NBIa=(NB^(2)a^(2)bv)/(R)` , towards left