Three identical square sheets, each of side s, are placed in the same uniform magnetic field of magnitude B. The sheets differ only in their orientation relative to the field lines:
• Sheet I: its plane is perpendicular to the field lines.
• Sheet II: its plane is tilted so that the normal to the sheet makes a 45∘ angle with the field direction.
• Sheet III: its plane is parallel to the field lines.
Assume the outward area vector for each sheet is defined by the right-hand rule.
(a) Rank the magnitude of the magnetic flux through the three sheets from greatest to least. Explain your reasoning without performing explicit calculations.
(b) State which sheet, if any, has zero magnetic flux and justify your answer in terms of the relationship between the field and the area vector.
(c) For Sheet II, describe qualitatively how doubling the side length s would affect the flux, assuming all other factors remain unchanged.