A coil of wire consists of 20 turns, or loops, each of which has an area of 1.5 x 10-3
m 2. A magnetic field is perpendicular to the surface of each loop at all times, so that Ø = Øo = 0°. At time to = 0s,
the magnitude of the field at the location of the coil is Bo = 0.050 T. At a later time t = 0.10s, the magnitude of the
field at the coil has increased to B = 0.060 T.
a. Find the average emf induced in the coil during this time.
b. What would be the value of the average induced emf if the magnitude of the magnetic field decreased
from 0.060 T to 0.050 T in 0.10s?
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a. .18
Kinger
To find the average induced emf in a coil, we 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 coil.
The magnetic flux (Φ) through a single loop of the coil is given by the product of the magnetic field (B) and the area of the loop (A). Since the magnetic field is perpendicular to the surface of each loop, the angle between the magnetic field and the area vector is always 0, so we can simplify the formula to Φ = B * A.
a. The average induced emf (ε) during the time interval Δt can be calculated using the formula ε = ΔΦ/Δt, where ΔΦ is the change in magnetic flux and Δt is the change in time.
To find ΔΦ, we need to calculate the initial magnetic flux Φo and the final magnetic flux Φ.
Φo = Bo * A = (0.050 T) * (1.5 x 10^(-3) m^2)
Φ = B * A = (0.060 T) * (1.5 x 10^(-3) m^2)
The change in magnetic flux ΔΦ is then:
ΔΦ = Φ - Φo
The change in time Δt is given as 0.10s.
Using the formula for average induced emf:
ε = ΔΦ/Δt = (Φ - Φo) / Δt
b. If the magnitude of the magnetic field decreases from 0.060 T to 0.050 T in 0.10s, we use the same approach as in part a to calculate the average induced emf.
Φo = Bo * A = (0.060 T) * (1.5 x 10^(-3) m^2)
Φ = B * A = (0.050 T) * (1.5 x 10^(-3) m^2)
The change in magnetic flux ΔΦ is then:
ΔΦ = Φ - Φo
Again, the change in time Δt is given as 0.10s.
Using the formula for average induced emf:
ε = ΔΦ/Δt = (Φ - Φo) / Δt
By following these steps, you can find the average induced emf in the coil for both scenarios.