Final answer:
The magnitude of the average induced voltage while the loop is pulled out of the magnetic field is 3.577 mV, which is calculated using the rate of change of magnetic flux through the loop over the time interval.
Step-by-step explanation:
When pulling a conducting loop out of a magnetic field, the induced voltage (or emf) in the loop is given by Faraday's Law of electromagnetic induction. This law states that the induced emf in a closed circuit is equal to the negative rate of change of the magnetic flux through the circuit.
To calculate the average induced voltage while the loop is pulled horizontally out of the magnetic field region during a time interval of 9.30 s, we can use the equation:
emf = - ∆ΦB / ∆t
The magnetic flux ΦB is the product of the magnetic field B and the area A of the loop that is perpendicular to the field. Since the magnetic field is homogeneous and the loop is being pulled out at a constant rate, we assume a linear decrease in flux.
First, calculate the initial flux:
ΦB(initial) = B * A
ΦB(initial) = 0.24 T * (π * (0.21 m)^2)
ΦB(initial) = 0.24 T * 0.1385 m2
ΦB(initial) = 0.03324 T*m2
The final flux ΦB(final) is zero since the loop is completely out of the magnetic field.
The rate of change of flux can then be calculated:
∆ΦB = ΦB(final) - ΦB(initial)
∆ΦB = 0 - 0.03324 T*m2
∆ΦB = -0.03324 T*m2
The average induced voltage is:
emf = - (-0.03324 T*m2) / 9.30 s
emf = 0.003577 volts or 3.577 mV (since the negative sign indicates direction, not magnitude)
Therefore, the magnitude of the average induced voltage while the loop is pulled out of the field is 3.577 mV.