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The figure shows the cross section of a toroid with a rectangular cross-section. The inner and outer radii of the toroid are R₁ and R2, and h is the height of the toroid. The coil consist on N turns and the core has a permeability u. The H-field lines and current i flowing through the toroid are shown. a) Apply Ampère's law to find the magnetic field intensity as a function of the distance r. Where r is the distance from the central axis of the toroid: 1) For r < R, in the air. 2) For R₁ <r < R₂ inside the toroid. 3) For r> R₂ in the air. b) Use the infinitesimal area element da = h dr shown to find the flux in the core. c) Find the inductance L using the flux linkage. | da