Here are the answers based on the described scenario:

Prompt 1: The magnetic field rotates to point parallel to the surface.
Answer: Induced emf will be positive.

Prompt 2: The magnetic field rotates to point exactly in the negative z-direction.
Answer: Induced emf will be negative.

Prompt 3: The magnetic field increases in magnitude.
Answer: Induced emf will be negative.

Prompt 4: The magnetic field reduces in magnitude.
Answer: Induced emf will be positive.

Do you want details or have any questions?

Here are 5 follow-up questions to expand your understanding:

1. How does the angle between the magnetic field and area vector affect the induced emf?
2. What is the mathematical relationship between the rate of change of magnetic flux and induced emf?
3. Why does the direction of magnetic field rotation affect the sign of the induced emf?
4. How would the induced emf change if the magnetic field was pointing along the positive z-direction?
5. What happens if both the magnitude and direction of the magnetic field change simultaneously?

Tip: The direction of induced emf is determined by Lenz's Law, which states that it always opposes the change in magnetic flux.