Two identical square metallic plates of side 12 cm are hinged along one common edge so that they form a foldable "book". Initially the plates are opened out to make a dihedral angle of 120° between their planes. A uniform magnetic field of 0.25 T is directed perpendicular to the plane of the first plate (Plate 1).
Attempt the following tasks:
a. (i) Obtain a general expression for the magnetic flux passing through each plate in terms of the given quantities and the dihedral angle ϕ between the plates.
b. (ii) Hence calculate the net magnetic flux linked with the two-plate system for ϕ=120°.
c. (iii) If the plates are slowly closed so that ϕ becomes 60°, determine the percentage change in the magnitude of the net flux.