1.6 The magnetic circuit of Fig. 1.25 consists of a core and a moveable plunger

Question

1.6

The magnetic circuit of Fig. 1.25 consists of a core and a moveable plunger of width lp, each of permeability mu. The core has cross-sectional area Ac and mean length lc. The overlap area of the two air gaps Ag is a function of the plunger position x and can be assumed to vary as Ag = Ac(1 - x/x0) You may neglect any fringing fields at the air gap and use approximations consistent with magnetic-circuit analysis. a. Assuming that mu rightarrow infinity, derive an expression for the magnetic flux density in the air gap Bg as a function of the winding current I and as the

Explanation / Answer

Hg = NI / 2g

Bc = (Ag/Ac)*Bg = Bg(1-x/X0)

2g.Hg + Hc.lc = NI

Bg = (mu0).Hg Bc = (mu).Hc

Solve to get:

Bg = NI / [ 2g + (mu0)/(mu) * (1 - x/X0) * (lc + lp) ]

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