Four closed surfaces are shown. The areas A_top and A_bot of the top and bottom faces and the magnitudes B_top and B_bot of the uniform magnetic fields through the top and bottom faces are given. The fields are perpendicular to the faces and are either inward or outward. Rank the surfaces according to the magnitude of the magnetic flux through the curved sides, least to greatest.

Question

Quizplus · Accepted Answer

The magnetic flux through a closed surface is given by the product of the magnetic field passing through the surface and the surface area. For surfaces 1 and 2, the magnetic field passing through the curved sides is zero, so their magnetic flux through the curved sides is also zero. 
For surfaces 3 and 4, the magnetic field passing through the curved sides is non-zero and the surfaces have the same geometry, so their magnetic flux through the curved sides will be proportional to the product of the magnitude of the magnetic field and the curved surface area. 
Since the same magnetic field passes through both curved sides of surface 3, and the same magnetic field passes through both curved sides of surface 4 but with a larger surface area, the magnetic flux through the curved sides of surface 4 will be greater than the magnetic flux through the curved sides of surface 3. 
Therefore, the surfaces should be ranked in order of increasing magnetic flux through the curved sides as: 1, 2, 3, 4. So, the correct answer is option B.

Four Closed Surfaces Are Shown