Question

The normal to a certain 1-m^2 area makes an angle of 60? with a uniform magnetic field.

The magnetic flux through this area is the same as the flux through a second area that is
perpendicular to the field if the second area is:
A. 0.866 m^2
B. 1.15 m^2
C. 0.5 m^2
D. 2 m^2
E. 1 m^2

Answer 1

The second area required to have the same magnetic flux as a 1 m² area at a 60° angle to the magnetic field would be 0.5 m², using the law of cosines in the calculation of magnetic flux.

Step-by-step explanation:

The student is asking about the comparison of magnetic flux through two different areas under the influence of a uniform magnetic field. To find the area required for the second surface to have the same magnetic flux as a 1 m² area at a 60° angle, we use the formula for magnetic flux Φ = B·A·cos(θ), where B is the magnetic field strength, A is the area, and θ is the angle between the magnetic field and the normal to the area.

For the first area which is 1 m² and at a 60° angle, the flux is Φ = B·(1 m²)·cos(60°) = B·(1 m²)·(0.5). For the second area to have the same flux but be perpendicular to the magnetic field (θ = 0°), the flux would be Φ = B·A. Thus, A = (B·(1 m²)·(0.5))/B = 0.5 m². Hence, the second area must be 0.5 m² to have the same magnetic flux as the first area, making the correct answer C. 0.5 m².