A conducting wire bent in the shape of semicircle has length L and moves in its plane with constant velocity v. A uniform magnetic field $\mathrm{B}$ exists in the direction perpendicular to the plane of the wire. The velocity makes an angle $45°$to the diameter joining free ends and the emf induced between the ends of the wire is $\mathrm{\Phi }=\mathrm{\alpha }\left(BvL\right)$. The value of constant $\mathrm{\alpha }$ is

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.