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?
30v
To calculate the maximum emf induced in the loop, we can use Faraday's Law of electromagnetic induction:
emf = -N * dΦ/dt
where:
- emf is the induced electromotive force
- N is the number of turns in the loop
- dΦ/dt is the rate of change of magnetic flux
First, we need to calculate the magnetic flux (Φ) through the loop. The magnetic flux is given by:
Φ = B * A * cos(θ)
where:
- 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 angle between the magnetic field and the normal to the loop is 90 degrees, so cos(θ) = 1. Therefore, the magnetic flux through the loop is:
Φ = B * A
Substituting the given values, we have:
Φ = 0.04 Tesla * 0.25 m^2
Φ = 0.01 Weber
Now, we can calculate the rate of change of magnetic flux (dΦ/dt) using the angular frequency (ω) of rotation:
dΦ/dt = ω * dΦ/dθ
Since the loop is rotating in a complete circle, the change in angle (dθ) is 2π radians. Therefore, we have:
dΦ/dt = ω * (dΦ/dθ)
dΦ/dt = 100 rad/s * (0.01 Weber / 2π radians)
dΦ/dt = 0.1591 Weber/s
Finally, we can calculate the maximum emf induced in the loop:
emf = -N * dΦ/dt
emf = -30 turns * 0.1591 Weber/s
emf = -4.773 Volts
The negative sign indicates that the direction of the induced emf is such that it opposes the change in magnetic field.