A circular plate of radius 0.5 m is placed perpendicular to the direction of the magnetic field of 0.5 Tesla. What is the change of flux in the plate if it rotates and its plane becomes parallel to the direction of the magnetic field?
To calculate the change of flux in the circular plate as it rotates and its plane becomes parallel to the magnetic field, we can use Faraday's Law of Electromagnetic Induction.
Faraday's Law states that the induced electromotive force (emf) in a closed loop is equal to the rate of change of magnetic flux passing through the loop.
The magnetic flux (Φ) passing through a surface is given by the equation:
Φ = B * A * cos(θ)
Where:
- B is the magnetic field strength in Tesla (given as 0.5 Tesla)
- A is the area of the surface in square meters (given as the area of a circle with radius 0.5 m = π * (0.5)^2 m^2)
- θ is the angle between the magnetic field direction and the normal to the surface (starts perpendicular initially, and becomes parallel)
The change in flux (ΔΦ) is obtained by subtracting the initial flux from the final flux:
ΔΦ = Φ_final - Φ_initial
Since the initial flux is when the plate is perpendicular to the magnetic field (θ = 90 degrees), we can calculate it as:
Φ_initial = B * A * cos(90°)
Since cos(90°) = 0, the initial flux becomes:
Φ_initial = B * A * 0 = 0
Next, we calculate the final flux when the plate is parallel to the direction of the magnetic field (θ = 0 degrees):
Φ_final = B * A * cos(0°)
Since cos(0°) = 1, the final flux becomes:
Φ_final = B * A * 1 = B * A
Substituting the values, we get:
Φ_final = 0.5 Tesla * π * (0.5)^2 m^2
Calculating Φ_final, we find:
Φ_final ≈ 0.3927 Tesla * m^2
Finally, we can calculate the change in flux:
ΔΦ = Φ_final - Φ_initial = 0.3927 Tesla * m^2 - 0 Tesla * m^2 = 0.3927 Tesla * m^2
Therefore, the change of flux in the circular plate as it rotates and its plane becomes parallel to the magnetic field is approximately 0.3927 Tesla * m^2.
To determine the change of flux in the circular plate as it rotates and its plane becomes parallel to the direction of the magnetic field, you need to understand the concept of magnetic flux.
Magnetic flux (Φ) is the measure of the magnetic field passing through a given surface. It is given by the equation:
Φ = B * A * cos(θ),
where B is the magnetic field strength, A is the area of the surface, and θ is the angle between the magnetic field and the normal to the surface.
In this case, the initial angle between the magnetic field and the normal to the circular plate is 90 degrees, as the plate is perpendicular to the magnetic field.
Initially, the magnetic flux passing through the plate can be calculated as:
Φ_initial = B * A * cos(90 degrees).
Since cos(90 degrees) = 0, the initial flux becomes zero:
Φ_initial = 0.
As the circular plate rotates and its plane becomes parallel to the direction of the magnetic field, the angle θ between the magnetic field and the normal to the plate becomes zero degrees. In this case:
Φ_final = B * A * cos(0 degrees).
Since cos(0 degrees) = 1, the final flux becomes:
Φ_final = B * A * 1.
Given that the radius of the circular plate is 0.5 m, the area of the plate (A) can be calculated as:
A = π * r^2,
A = π * (0.5 m)^2,
A = π * 0.25 m^2.
Substituting the values into the equation for the final flux:
Φ_final = 0.5 Tesla * (π * 0.25 m^2) * 1,
Φ_final = 0.125 π Tesla-m^2.
So, the change in flux (ΔΦ) is the difference between the final and initial flux:
ΔΦ = Φ_final - Φ_initial,
ΔΦ = 0.125 π Tesla-m^2 - 0,
ΔΦ = 0.125 π Tesla-m^2.
Therefore, the change of flux in the plate as it rotates and becomes parallel to the magnetic field is 0.125 π Tesla-m^2.