Final answer:
The correct formula for motional emf when B, length (ℓ), and velocity (v) are not mutually perpendicular is “emf = Bℓvsinθ”, which factors in the angle between v and B.
Step-by-step explanation:
When a conductor moves in a magnetic field and the velocity of the conductor, the length of the conductor, and the magnetic field are not mutually perpendicular, the correct formula to calculate the motional emf (electromotive force) is emf = Bℓvsinθ, where:
- B is the magnetic field strength,
- ℓ is the length of the conductor,
- v is the velocity of the conductor, and
- θ (theta) is the smallest angle between v and B.
This equation signifies that the induced emf is directly proportional to the component of the velocity that is perpendicular to the magnetic field. If the velocity of the conductor is entirely perpendicular to the magnetic field, θ becomes 90 degrees and sinθ becomes 1, reducing the formula to emf = Bℓv, which is the expression for motional emf without considering angles between the vectors.