ECE 330 homework assignment #4, due in Mid-term examination Problem 1 For the magnetic circuit in Fig. 1 below, the upper part with winding is fixed, and the lower part is movable (up and down only). Take into account the effect of fringing in the air gaps, and core reluctance (the mean length of flux path in iron core is lc). a) Find the expressions for flux linkage, energy, and force of electric origin. b) Calculate the force for the following condition: N = 300, i = 7 A, a = 3 cm, d = 2 cm, lc = 40 cm, g = 0.5 cm, and the relative permeability of the iron core is µr = 1500.

Fig. 1 Problem 2 For the structure drawn in Fig. 2 below, the movable member is constrained to move left and right only as indicated in the figure where “x” is the distance to the right edge of the movable member. The large member with the coil is fixed, and the depth into the page for both members is 2 cm. The gap g is 2 mm, and the number of turns N = 200. Neglect fringing in the gaps, and core reluctance.

a) Find the expressions for the flux linkage, energy, co-energy, and force of electric origin.

b) Calculate the force with i = 10 A, x = 5 cm (maximum value of x is 8 cm).

Fig. 2 Text problem 4.15 Text problem 4.19 Text problem 4.26

N

g g

Depth d into page

a

i

a

a

a

x

g

g

i

N

8 cm