Marks: 4
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?
B*A
A is the plate area in m^2.
Answer is in Webers
To calculate the change of flux in the circular plate, we need to use the formula for magnetic flux (Φ):
Φ = B * A * cos(θ),
where B is the magnetic field, A is the area, and θ is the angle between the magnetic field and the normal to the surface.
In this case, initially, the plate is perpendicular to the magnetic field, so the angle θ is 90 degrees. The flux can be calculated as:
Φ1 = B * A1 * cos(90) ---(1)
where A1 is the area of the circular plate when it is perpendicular to the magnetic field.
Next, the plate rotates, and its plane becomes parallel to the magnetic field. In this case, θ becomes 0 degrees. The flux can be calculated as:
Φ2 = B * A2 * cos(0) ---(2)
where A2 is the area of the circular plate when it is parallel to the magnetic field.
Now, let's calculate the areas A1 and A2 of the circular plate using the given radius:
A = π * r^2,
where r is the radius of the circular plate.
Substituting the given radius of 0.5 m in the above equation, we can find the areas:
A1 = π * (0.5)^2 = 0.7854 m^2,
A2 = π * (0.5)^2 = 0.7854 m^2.
Now, substituting the values of B, A1, and A2 into equations (1) and (2), we can find the fluxes:
Φ1 = 0.5 * 0.7854 * cos(90) = 0,
Φ2 = 0.5 * 0.7854 * cos(0) = 0.3927 Tesla*m^2.
Therefore, the change of flux in the circular plate when it rotates and its plane becomes parallel to the magnetic field is 0.3927 Tesla*m^2.