Find the current in the wire PQ for the configuration shown in Fig. Wire PQ has negligible resistance. B, the magnetic field is coming out of the paper. `theta` is a fixed angle made by PQ travelling smoothly over two conducting parallel wires seperated by a distance d.

Explanation

In Fig. PQ is a wire of negligible resistance travelling smoothly over two conducting parallel wires X and Y separated by distance (d). `theta` is fixed angle made by PQ and B is strength of magnetic field perperdicular to the plane of paper and outwards. Motional electric field `= upsion B`.
Its direction is along 0 K, perpendicular to `vec upsilon` and `vec B`.
`:.` e.m.f. induced in wire PQ
e = length `PQ xx ` motional electric field along QP
`= ((d)/(sin theta)) xx upsilon B sin theta = d upsilon B`
current in the wire, `I = (e)/(R ) = (d upsilon B)/(R )`