Question

For problem f), the current value is not on the picture. How to find the force and get the flux without current since F=Ni. Same for problem g)

5. (34 points) A ferromagnetic core with a constant relative permeability of 2000 is shown in the following figure. The core depth is 6 cm, and all dimensions are as shown in the figure. The air gap length on the leftmost column of the core is 0.01 cm. Because of fringing effects, the effective area of the air gaps is 8 percent larger than its physical size. If there are 150 turns in the coil wrapped around the center leg of the core, a) Draw the magnetic equivalent circuit of the system. (3 points) b) Find 1, l2, 13, l4, Is, l6, and l in meters. (7 points) c) Find cross-sectional areas in each region of the core in mand name them as A, A2, A3, A, As, Ae6, A7, as well as Aagfor the air gap considering the fringing effects. (8 points) d) Find all reluctances in the equivalent circuit. (8 points) e Find the magnetomotive force produced by the coil. (2 points) f Find the flux flowing through the air gap. (3 points) g) Find the flux density in the air gap. (3 points) 10 em 0.01 em 30 em 150 turns Core Depth-6 em

Answer 1

Relative Permeability = 2000 core depth = 6cm Air gap length = 0.01cm Effective area of air gap = 8% larger than physical size Turns = 150 We cannot find without knowing the current. Current has to be known = > let us take current as 1A = > This core can be derived into 4 parts. Let R_1 be the reluctance of the left hand portion of the core R_2 be the reluctance of the left hand air gap R_3 be the reluctance of the right hand portion R_4 be the reluctance of the centre leg of the core. Then \r\n total reluctance of the core is R_TOTAL = R_4 + (R_1 + R_2) times R_3/R_1 + R_2 + R_3 \r\n l_1 = 35 + 45 = 80cm = 0.8m l_2 = 0.01 times 10^-2 = 0.0001 l_3 = 35 + 30 = 65cm = 0.65m l_4 = 35 times 10^-2 = 0.35m R_1 = l_1/ mu_r mu_0A = 0.8/2000 times