Q$2.$ An electromagnetic device has a magnetic circuit that consists of three sections in a series of uniform cross sections.

Section A: Length $12$ cm and cross$-$sectional area $1\mathrm{.}5c{m}^2$

Section B: Length $6$ cm and cross$-$sectional area $0\mathrm{.}8c{m}^2$

Section C: Air gap length $0\mathrm{.}25$ mm and cross$-$sectional area $1\mathrm{.}5c{m}^2$

Each Sections A and Section B has magnetic characteristics as follows:

Table Q$1$

$\backslash$table$[[H(A\frac{T}{m}),100,210,340,500,800,1500],[$B $($Tesla$),0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}6,0\mathrm{.}8,1\mathrm{.}0,1\mathrm{.}2]]$

$($i$)$ Sketch the magnetic equivalent circuit of the system.

$($ii$)$ Determine the current required in the $5000-$tum coil that is wound at Section B to establish flux density $0\mathrm{.}4$ T in the air gap. Neglect magnetic flux leakage and fringing effect. You may sketch or interpolate the B$-$H curve from the table.