Evelyn wears glasses whose wire frames are shaped like to circles, each with an area of 7.0x10^-4 m^2. The horizontal component of the earths' magnetic field in Evelyn's hometown is 4.9x10^-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, which states that the induced electromotive force (emf) in a closed loop is equal to the rate of change of magnetic flux through the loop.
First, let's calculate the magnetic flux through one eyepiece. Given that each eyepiece has a circular wire frame with an area of 7.0x10^-4 m^2, the magnetic flux (Φ) through one eyepiece can be calculated using the equation:
Φ = B * A
Where B is the magnetic field and A is the area.
Φ = (4.9x10^-5 T) * (7.0x10^-4 m^2)
Φ = 3.43x10^-8 T∙m^2
Next, we need to determine the rate of change of magnetic flux, which is equal to the change in magnetic flux divided by the change in time.
The change in magnetic flux (ΔΦ) is equal to the final magnetic flux minus the initial magnetic flux.
ΔΦ = Φ_final - Φ_initial
Since we are interested in the induced voltage as Evelyn rotates her head back and forth, the final magnetic flux is equal to the initial magnetic flux.
ΔΦ = Φ - Φ
ΔΦ = 0
Therefore, there is no change in magnetic flux between the initial and final positions of Evelyn's head movement.
Now, let's calculate the induced voltage (emf) using Faraday's Law:
emf = -N * (ΔΦ/Δt)
Where N is the number of turns in the wire frame and Δt is the change in time.
Given that the number of turns in each eyepiece's wire frame is not mentioned in the question, we'll assume it to be 1 for simplicity.
emf = -1 * (0/0.5s)
emf = 0 V
Therefore, the induced voltage in the wire frame of one eyepiece is 0 volts. This means that there is no induced voltage as Evelyn rotates her head back and forth in this situation.