With a magnetic field perpendicular to a single 13.2 cm diameter circular loop of copper wire decreases uniformly from .670 T to zero. If the wire is 2.25 mm in diameter how much charge moves past a point in the coil during this operation?
To determine the amount of charge that moves past a point in the coil during this operation, 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 magnetic flux (Φ) can be calculated as the product of the magnetic field (B) and the area (A) of the coil. In this case, since the magnetic field is decreasing uniformly from 0.670 T to zero, we can use the average value of the magnetic field.
First, let's calculate the average magnetic field (B_avg):
B_avg = (B_initial + B_final) / 2
B_avg = (0.670 T + 0 T) / 2
B_avg = 0.335 T
Next, let's calculate the area of the coil (A). Since the coil is circular, the area can be calculated using the formula:
A = π * r^2
r = diameter / 2
r = 13.2 cm / 2
r = 6.6 cm = 0.066 m
A = π * (0.066 m)^2
A = 0.0137 m^2
Now, we can calculate the magnetic flux (Φ):
Φ = B_avg * A
Φ = 0.335 T * 0.0137 m^2
Φ = 0.00459 Wb (webers)
Finally, we can use Faraday's Law to calculate the amount of charge moved:
EMF = -dΦ/dt
dΦ = change in magnetic flux = Φ_final - Φ_initial
dt = change in time
Since the magnetic field decreases uniformly from .670 T to zero, we can assume that the change in magnetic field is linearly proportional to time, and the time it takes to go from the initial field to zero is not given. Therefore, we cannot determine the exact value of the charge moved.
However, if we assume a constant rate of change and know the time it takes to go from the initial field to zero, we can use the equation:
Q = ∫(EMF) dt
where ∫ represents integration.
By substituting and integrating, we can find the total charge moved.