To monitor the breathing of a hospital patient, a thin belt is girded around the patient's chest. The belt is a 200-turn coil. When the patient inhales, the area encircled by the coil increases by 45.0 cm2. The magnitude of the Earth's magnetic field is 50.0 μT and makes an angle of 28.0° with the plane of the coil. Assuming a patient takes 1.72 s to inhale, find the average induced emf in the coil during this time interval.
µV
To find the average induced emf in the coil, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced emf is given by the equation:
ε = -N * ΔΦ/Δt
where ε is the induced emf, N is the number of turns (in this case, 200 turns), ΔΦ is the change in magnetic flux, and Δt is the time interval.
First, we need to calculate the change in magnetic flux (ΔΦ). The magnetic flux through the coil is given by the equation:
Φ = B * A * cos(θ)
where B is the magnitude of the Earth's magnetic field (50.0 μT), A is the area encircled by the coil (45.0 cm²), and θ is the angle between the magnetic field and the plane of the coil (28.0°).
Convert the magnetic field to Tesla:
B = 50.0 μT = 50.0 * 10^(-6) T
Convert the area to square meters:
A = 45.0 cm² = 45.0 * 10^(-4) m²
Now we can calculate the change in magnetic flux:
ΔΦ = (B * A * cos(θ)) - (B * A * cos(0°))
= B * A * (cos(θ) - cos(0°))
Next, we can calculate the time interval (Δt), which is given as 1.72 s.
Finally, we can substitute the values into the formula:
ε = -N * ΔΦ/Δt
= -200 * [(B * A * (cos(θ) - cos(0°))) / Δt]
Evaluate the expression to find the average induced emf (ε) in microvolts (µV).