A wire loop of radius 0.10m lies so that an external magnetic field of magnetic 0.50T is perpendicular to the loop. the field changes its magnitude to 0.01 T in 2.5 s. find the magnitude and the direction of the average induced emf in the loop during this time.
EMF= d flux/dt= (.5-.01)/PI*r^2*2.5
direction? You will have to look at the drawing and use your hand rules.
To find the magnitude and direction of the average induced electromotive force (emf) in the loop, you can use Faraday's Law of electromagnetic induction. According to Faraday's Law, the induced emf in a conducting loop is equal to the rate of change of magnetic flux through the loop.
First, let's calculate the initial and final magnetic flux through the loop.
1. Initial magnetic flux (Φ₁):
The magnetic flux through a loop is given by the product of the magnetic field strength (B) and the area (A) of the loop. Since the magnetic field is perpendicular to the loop, the angle between the magnetic field and the area vector is 0 degrees. Therefore, the formula for magnetic flux simplifies to:
Φ₁ = B₁ * A
where B₁ is the initial magnetic field strength and A is the area of the loop.
Substituting the given values:
B₁ = 0.50 T (given)
A = π * r² = π * (0.10 m)² = 0.0314 m² (using the formula for the area of a circle)
Φ₁ = (0.50 T) * (0.0314 m²) = 0.0157 Wb (webers)
2. Final magnetic flux (Φ₂):
By following the same process as above, we can calculate the final magnetic flux through the loop as:
Φ₂ = B₂ * A
where B₂ is the final magnetic field strength (0.01 T) and A is the area of the loop (0.0314 m²).
Φ₂ = (0.01 T) * (0.0314 m²) = 0.000314 Wb
Now, we can use Faraday's Law to calculate the average induced emf (ε) in the loop during the time interval.
Faraday's Law states that the induced emf is equal to the rate of change of magnetic flux, which can be expressed as:
ε = (Φ₂ - Φ₁) / Δt,
where Δt is the change in time from the initial to the final flux.
Substituting the calculated values:
ε = (0.000314 Wb - 0.0157 Wb) / 2.5 s
ε = -0.01539 V
The negative sign indicates that the induced emf opposes the change in magnetic flux.
Therefore, the magnitude of the average induced emf in the loop during this time is approximately 0.01539 V, and its direction is opposite to the change in flux.