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 direction of the magnetic field in the curved sides can be determined using the right-hand rule. Imagine gripping the surface with your right hand so that your fingers curl along the curved surface. Your thumb will point in the direction of the magnetic field. 
For surface 1, the magnetic field is outward through the top face and inward through the bottom face. Using the right-hand rule, the direction of the magnetic field through the curved sides is clockwise, resulting in a negative flux. 
For surface 2, the magnetic field is inward through both faces. Using the right-hand rule, the direction of the magnetic field through the curved sides is counterclockwise, resulting in a positive flux.
For surface 3, the magnetic field is inward through the top face and outward through the bottom face. Using the right-hand rule, the direction of the magnetic field through the curved sides is counterclockwise, resulting in a positive flux.
For surface 4, the magnetic field is outward through both faces. Using the right-hand rule, the direction of the magnetic field through the curved sides is clockwise, resulting in a negative flux. 
Therefore, the surfaces can be ranked in increasing order of magnetic flux through the curved sides as follows: 3, 4, 1, 2. This matches option B.

Four Closed Surfaces Are Shown