Evelyn wears glasses whose wire frames are shaped like to circles, each with an area of 8.0x10^-4 m^2. The horizontal component of the earths' magnetic field in Evelyn's hometown is 3.9x10^-5 T. If Evelyn turns her head back and forth, rotating it through 90degrees every 0.5s, what is the induced voltage in the wire frame of one eyepiece
To find the induced voltage in the wire frame of one eyepiece, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced electromotive force (EMF) in a closed loop is equal to the rate of change of magnetic flux through the loop.
In this case, the loop is the wire frame of one eyepiece, and the magnetic flux through the loop is given by the product of the magnetic field and the area of the loop.
First, let's calculate the magnetic flux through one eyepiece:
Magnetic flux (Φ) = Magnetic field (B) * Area (A)
Given:
Area of each eyepiece (A) = 8.0x10^-4 m^2
Magnetic field (B) = 3.9x10^-5 T (horizontal component of Earth's magnetic field)
Φ = (3.9x10^-5 T) * (8.0x10^-4 m^2)
Φ = 3.12x10^-8 Tm²
Now, we have to calculate the rate of change of magnetic flux. Since Evelyn is rotating her head back and forth, and each rotation takes 0.5 seconds, the rate of change of magnetic flux can be determined by dividing the change in magnetic flux by the time taken.
Change in magnetic flux (ΔΦ) = (Final magnetic flux - Initial magnetic flux)
Time taken (Δt) = 0.5 seconds
ΔΦ/Δt = (3.12x10^-8 Tm² - 0) / (0.5 s)
ΔΦ/Δt = 6.24x10^-8 Tm²s⁻¹
Finally, the induced voltage (V) can be determined by multiplying the rate of change of magnetic flux by the number of turns in the wire frame (assuming there is only one turn):
V = ΔΦ/Δt * N
Assuming N = 1 (one turn):
V = (6.24x10^-8 Tm²s⁻¹) * 1
V = 6.24x10^-8 V
Therefore, the induced voltage in the wire frame of one eyepiece is 6.24x10^-8 V.