Q.How will you induce an emf by changing the area enclosed by the coil?

Setup and derivation. A conducting rod of length l slides with velocity v along the rails of a fixed U-shaped rectangular metallic frame, immersed in a uniform field $\vec B$ perpendicular to the frame's plane. As the rod slides over a small time dt, the enclosed loop area shrinks by $l\times(v\,dt)$, so the flux change is $d\Phi_B=B\,l\,v\,dt$, giving $d\Phi_B/dt = Blv$ and hence the induced emf

-- exactly the same motional-emf formula obtained via the Lorentz-force derivation, now re-derived from the changing-AREA (flux) viewpoint, confirming both routes are fully consistent. If the loop closes through resistance R, the induced current is $i=Blv/R$, its direction given by Fleming's right hand rule. …