The normal to a certain 1-m² area makes an angle of 60 $\degree$ 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 m² B) 1.15 m² C) 0.5 m² D) 2 m² E) 1 m²

Question

Quizplus · Accepted Answer

Since the normal to the first area makes an angle of 60∘ with the magnetic field, the flux through the first area is given by:
Φ1 = A1 * B * cos(60∘)
where A1 is the area, B is the magnetic field, and cos(60∘) = 0.5

For the flux through the second area to be the same, we need to have:
Φ2 = A2 * B

Equating the two fluxes and substituting for cos(60∘), we get:
A1 * B * 0.5 = A2 * B
Simplifying, we find that:
A2 = 0.5 * A1

Therefore, the second area must be half as large as the first area.
Among the answer choices, only option C has an area that is half of 1 m², so the answer is C.

The Normal to a Certain 1-M2 Area Makes an Angle °\degree°

The Normal to a Certain 1-M² Area Makes an Angle $\degree$