A circular loop with 30 turns and area of 0.25 m2 rotates at 100 rad/s. The axis of rotation of the loop is perpendicular to the direction of the magnetic field of 0.04 Tesla. What is the maximum emf induced in the loop?
15 V
30 V
45 V
60 V
I got 15 V but that doesn't seem quite right
ℰ(max) =NBAω =30•0.04•0.25•100 = 30
To determine the maximum emf induced in the loop, we can use Faraday's law of electromagnetic induction. This law states that the emf induced in a loop is equal to the rate of change of magnetic flux through the loop.
The magnetic flux through a loop is given by the equation:
Φ = B * A * cos(θ)
Where:
- Φ is the magnetic flux through the loop
- B is the magnetic field strength
- A is the area of the loop
- θ is the angle between the magnetic field and the normal to the loop
In this case, the area of the loop is given as 0.25 m2, the magnetic field strength is 0.04 Tesla, and the angle between the magnetic field and the normal to the loop is 90 degrees (since the axis of rotation is perpendicular to the magnetic field).
Φ = (0.04 Tesla) * (0.25 m2) * cos(90 degrees)
Φ = 0.04 * 0.25 * 0
Φ = 0
Since the magnetic flux through the loop is zero, the rate of change of magnetic flux is also zero. Therefore, there is no emf induced in the loop.
So none of the answer choices provided (15V, 30V, 45V, 60V) are correct in this case.