Initially a rectangular coil with length vertical is moving out with constant velocity 'v' in a constant magnetic field 'B' towards right. Now the same coil is rotated through $90^{\circ}$ in same plane in same magnetic field $B$ and the coil is moving with same velocity $v$. The magnitude of induced e.m.f. is now

For a conductor moving perpendicular to a magnetic field, the induced e.m.f. is governed by $\varepsilon = B l v$, where $l$ is the length cutting flux lines perpendicularly.

The rectangular coil has dimensions $L$ (length) and $w$ (width). Initially, with $L$ vertical, the induced e.m.f. is $\varepsilon_{\text{initial}} = B L v$.

After a $90^\circ$ rotation, the vertical side becomes $w$, so $\varepsilon_{\text{final}} = B w v$.

The magnitudes compare as $\varepsilon_{\text{final}} > \varepsilon_{\text{initial}}$ if $w > L$, $\varepsilon_{\text{final}} < \varepsilon_{\text{initial}}$ if $w < L$, and are equal if $w = L$. Since no dimensions are specified, all outcomes are possible, leading to answer $\boxed{D}$.