A coil is made up of 19 square loops with the sides equal to 5.3 cm. The coil is placed in a uniform 350 mT magnetic field with the axis of the coil parallel to the magnetic field. If the field reverses direction in 0.17 seconds, what is in volts, the average emf induced in the coil?
V = N*A*dB/dt
= (# of loops)*(Area)*(0.35 T)/(0.17 s)
.688
To find the average emf induced in the 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 through a loop can be calculated as the product of the magnetic field strength (B), the area of the loop (A), and the cosine of the angle between the magnetic field and the normal to the loop (θ).
The area of each square loop is equal to the square of the side length (squared), so in this case, the area of each loop would be (5.3 cm)^2 = 28.09 cm^2.
Since the coil is made up of 19 loops, the total area of the coil would be 19 times the area of a single loop.
Total Area of the coil = 19 * 28.09 cm^2
Now, let's calculate the average emf induced in the coil using the given values.
Magnetic field strength, B = 350 mT = 350 * 10^(-3) T (Telsa)
Change in magnetic field, ΔB = 2 * B (since the field is reversing its direction)
Time duration, Δt = 0.17 seconds
Now we can calculate the average emf using Faraday's law:
Average emf = ΔΦ/Δt
= (ΔB * A * cosθ) / Δt
= (2 * B * A * cosθ) / Δt
Substituting the values, we get:
Average emf = (2 * (350 * 10^(-3) T) * (19 * 28.09 cm^2) * cosθ) / (0.17 seconds)
Since the axis of the coil is parallel to the magnetic field, the angle between the magnetic field and the normal to the loop is 0 degrees. Therefore, cosθ = 1.
Average emf = (2 * (350 * 10^(-3) T) * (19 * 28.09 cm^2) * 1) / (0.17 seconds)
Now, convert the given area from cm² to m²:
Average emf = (2 * (350 * 10^(-3) T) * (19 * 0.002809 m²) * 1) / (0.17 seconds)
Simplifying,
Average emf = 1.336 V
Therefore, the average emf induced in the coil is approximately 1.336 volts.