The arm `PQ` of the rectangular conductor is moved from `x=0`, outwards in the uniform magnetic field which extends from `x=0` to `x=b` and is zero for `x gt b` as shown. Only the arm `PQ` possess substantial ressitance `r`. Consider the situation when the arm `PQ` is pulled outwards from `x = 0` to `x = 2b`, and is then moved back to `x = 0` with constant speed `v`. Obtain expression for the flux, the induced emf, the force necessary to pull the arm and the power dissipated as Joule heat. Sketch the variation of these quantities with distance.

Explanation

Let us first consider the forward motion from `x = 0` to `x = 2b`. The flux `phi_(B)` linked with the circuit `SPQR` is
The induced emf is,
`epsilon = -(d phi)/(dt) = -Bl" "0 le x le b`
`epsilon = 0 b le x le 2b`
When the induced emf is non zero,
the current `I` is `I = (Blv)/(r )` (in magnitude)