I have a 250- turn circular coil of wire, 0.10 m in diameter, perpendicular to a 0.050 T magnetic field as shown below. I flip the coil 180 degrees in 1/30 of a second. What is the average voltage created across the ends of the coil?
A. -6.0 V
B. -12 V
C -3.0 V
D. -24 V
I think we might be in the same physics class. For this question I put -12 and was incorrect...what did you put so we can get the answer choices down to two options?
i put -6.0 V. i think that's it
no
To calculate the average voltage created across the ends of the coil, we can use Faraday's Law of electromagnetic induction, which states that the induced voltage in a coil is equal to the rate of change of magnetic flux through the coil.
First, we need to calculate the magnetic flux through the coil, which is given by the formula:
Φ = B * A * cosθ
Where:
Φ = magnetic flux
B = magnetic field strength (0.050 T)
A = area of the coil = π * (radius of the coil)^2 = π * (0.10 m / 2)^2
θ = angle between the magnetic field and the normal to the loop (perpendicular in this case, so θ = 0 degrees)
Substituting the values into the formula, we have:
Φ = 0.050 T * π * (0.10 m /2)^2
= 0.050 T * π * (0.05 m)^2
= 0.050 T * π * 0.0025 m^2
= 0.00019635 Wb
Next, we need to calculate the rate of change of magnetic flux. Since the coil is flipped 180 degrees in 1/30 of a second, we can calculate the change in flux per unit time:
ΔΦ/Δt = (Φ final - Φ initial) / t
= (0 - 0.00019635 Wb) / (1/30 s)
= -0.00019635 Wb / (1/30 s)
= -0.00019635 Wb * (30 s)
= -0.0058905 Wb/s
Finally, the average voltage is given by:
V = -N * ΔΦ/Δt
Where:
V = voltage
N = number of turns in the coil (250)
Substituting the values:
V = -250 * (-0.0058905 Wb/s)
= 1.4726 V
Since the voltage is negative, the correct answer is:
A. -6.0 V