Problem:
A fixed 16.2-cm-diameter wire coil is perpendicular to a magnetic field 0.79 T pointing up. In 0.15 s , the field is changed to 0.34 T pointing down.
Part A:
What is the average induced emf in the coil?
To find the average induced emf in the coil, we need to use Faraday's law of electromagnetic induction, which states that the electromotive force (emf) induced in a circuit is equal to the rate of change of the magnetic flux through the circuit.
The formula for the induced emf is given by:
emf = -N * dΦ/dt
Where emf is the induced emf, N is the number of turns in the coil, dΦ is the change in magnetic flux, and dt is the time interval over which the change occurs.
In this problem, we are given the following information:
Diameter of the wire coil = 16.2 cm
Radius of the wire coil (r) = diameter/2 = 16.2/2 = 8.1 cm = 0.081 m
Magnetic field initially = 0.79 T (pointing up)
Magnetic field finally = 0.34 T (pointing down)
Time interval (dt) = 0.15 s
To find the average induced emf, we need to calculate the change in magnetic flux (dΦ) and the number of turns (N) in the coil.
First, let's find the change in magnetic flux (dΦ):
The formula for magnetic flux (Φ) through a coil is given by:
Φ = B * A
Where Φ is the magnetic flux, B is the magnetic field, and A is the area of the coil.
The area of the coil can be calculated using the formula:
A = π * r^2
Plugging in the values, we get:
A = π * (0.081 m)^2
Now, let's calculate the initial and final magnetic flux (Φ_initial and Φ_final):
Φ_initial = B_initial * A
Φ_final = B_final * A
Substituting the values, we have:
Φ_initial = 0.79 T * π * (0.081 m)^2
Φ_final = 0.34 T * π * (0.081 m)^2
Next, let's find the change in magnetic flux (dΦ) by subtracting Φ_initial from Φ_final:
dΦ = Φ_final - Φ_initial
Finally, let's substitute the values of dΦ, N, and dt into the formula for the average induced emf to find the answer:
emf = -N * dΦ/dt
Note: The negative sign represents the direction of the induced current in the coil, which is determined by Lenz's law.
Calculating these values will give us the average induced emf in the coil.