A rectangular loop with 100 turns and area of 0.12 m2 rotates at 100 rad/s. The axis of rotation of the square is perpendicular to the direction of the magnetic field of 0.025 Tesla. What is the maximum emf induced in the loop?
Choose one answer.
a. 30 V
b. 94 V
c. 188 V
d. 250 V
30 V
To find the maximum emf induced in the loop, we can use Faraday's law of electromagnetic induction, which states that the emf (ε) induced in a loop is equal to the rate of change of magnetic flux (Φ) through the loop.
The magnetic flux through the loop can be calculated using the formula:
Φ = B * A * cos(θ)
Where:
- B is the magnetic field strength (0.025 Tesla)
- A is the area of the loop (0.12 m^2)
- θ is the angle between the magnetic field and the normal to the loop, which is 90 degrees since the axis of rotation is perpendicular to the magnetic field.
Substituting these values into the formula, we get:
Φ = 0.025 * 0.12 * cos(90°)
Φ = 0.003 T·m^2
Now, we can calculate the maximum emf induced in the loop using Faraday's law:
ε = dΦ/dt
Where:
- dΦ/dt represents the rate of change of magnetic flux through the loop.
- In this case, the loop rotates at a constant angular velocity (ω) of 100 rad/s, so the rate of change of magnetic flux is given by:
dΦ/dt = -ωΦ (negative sign due to Faraday's law)
Substituting the values:
ε = -100 * 0.003
ε = -0.3 V
Therefore, the maximum emf induced in the loop is 0.3 V (with negative sign).
Since none of the given options match the calculated value, it seems there might be an error in the question or the answer choices provided.