Question

Consider the core given in Fig.1. Relative permeability of the core material is 2000. a) What should be the coil current to achive a flux density of 2T when x-0. State your assumptions in the calculations b) Current in the coil is kept constant at the value found in part (a) as the armature moves to x-2 mm. What is the flux density when x-2 mm?

Answer 1

This problem is all about applying formulae properly.

B = 2T, A = 5.cm^2 = 5 times 10^-4 m^2 Therefore phi = BA = 10^-3 wb = 0.001 wb Reluctance = R = l/mu_0 mu_r A = 20 times 10^-2/ 4 pi 10^-7 times 2000 times 5 times 10^-4 = 159155 AT/wb Now, AT = phi times R = > N times I = phi times R = > 100 times I = 0.001 times 159155 = > I = 1.592 A when x = 2 mms(+ ani-gap) R = 18.8 times 10^-2/4 pi times 10^-7 times 2000 times 5 times 10^-4 + 0.02 times 10^-2/4 pi times 10^-7 times 5 times 10^-4 = 467916 AT/wb \r\n Therefore phi = NI/R = 100 times 1.592/467916 = 3.4023 times 10^-4 wb Therefore B = phi /A = 3.4023 times 10^-4/5 times 10^-4 = 0.68 T E = 1/2 phi^2 R For x = 0, E = 1/2 times 0.001^2 times 159155 = 0.08 J