The electromotive force (e.m.f.) induced in a wire moving in a magnetic field will be the same in magnitude but opposite in direction when the wire is moved downwards compared to upwards. Here's why:

Faraday's Law of Electromagnetic Induction:

Faraday's Law states that the magnitude of the induced e.m.f. is proportional to the rate of change of magnetic flux through the loop. The direction of the induced e.m.f. is determined by Lenz's Law, which states that the induced current will flow in a direction that opposes the change in magnetic flux.

Moving the Wire:

* Downwards: When the wire moves downwards, the magnetic flux through the loop increases. To oppose this increase, the induced current will create a magnetic field that opposes the original magnetic field. This requires the induced current to flow in a specific direction.

* Upwards: When the wire moves upwards, the magnetic flux through the loop decreases. To oppose this decrease, the induced current will create a magnetic field that reinforces the original magnetic field. This requires the induced current to flow in the opposite direction compared to when the wire moved downwards.

Conclusion:

The magnitude of the e.m.f. remains the same because the rate of change of magnetic flux is the same in both cases. However, the direction of the e.m.f. is reversed due to the opposite directions of the induced magnetic field required to oppose the change in magnetic flux.