A 17.0 cm diameter circular loop of wire is in a 1.35 T magnetic field. It is removed from the field in 0.190 s. What is the average induced emf?
To find the average induced emf, you can use Faraday's law of electromagnetic induction, which states that the induced emf is equal to the rate of change of magnetic flux through the surface bounded by the loop.
The formula to calculate the average induced emf is:
Emf = -N * ΔΦ/Δt
where:
- Emf is the induced electromotive force (emf)
- N is the number of turns in the wire loop
- ΔΦ is the change in magnetic flux
- Δt is the time taken for the change in magnetic field
In this case, we have a circular loop of wire with a diameter of 17.0 cm, so the radius, r, can be calculated as:
r = diameter/2 = 17.0 cm / 2 = 8.5 cm = 0.085 m
We also have a magnetic field of 1.35 T and a time interval of 0.190 s.
First, let's calculate the change in magnetic flux (ΔΦ):
ΔΦ = 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's surface
Since the loop is a circle, the area is given by:
A = π * r^2
In this case, the angle (θ) is 0 degrees because the magnetic field is perpendicular to the loop's surface. So, cos(θ) = 1.
Substituting the given values into the formulas:
A = π * (0.085 m)^2
A ≈ 0.0226686473 m²
ΔΦ = (1.35 T) * (0.0226686473 m²) * 1
ΔΦ ≈ 0.0306466908 Wb (webers)
Now, let's calculate the average induced emf using the formula:
Emf = -N * ΔΦ/Δt
In this case, we are not given the number of turns (N) in the wire loop. Without that information, we cannot calculate the exact value of the average induced emf.