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magnetic field inside a toroid is given by H =NI/(2*r avg ) where N=30 is the #

ID: 1658836 • Letter: M

Question

magnetic field inside a toroid is given by H =NI/(2*ravg) where N=30 is the # of turns (only 2 turns shown in the picture for clarity), I is the current, and ravg is the average of the

outer and inner radii.

a. Using the measured B-H data, estimate the relative permeability (r) of the core

for small fields—obtain from the slope of the linear portion of the curve.

b. Calculate the magnetic field (H) and magnetic flux density (B) inside the magnetic

core for a current of 0.2 A in the inductor.

c. Calculate the magnetic field (H) and magnetic flux density (B) inside the magnetic

core for a current of 5 A in the inductor (careful! will be in the nonlinear regime).

R2 R1 6.3 mm 12.7 mm 1.5 1 0.5 0.5 -1 1.5 4000 -2000 2000 4000 6000 H (A/m)

Explanation / Answer

R1 = 6.3mm/2 = 3.15 mm

R2 = 12.7mm/2 = 6.35 mm

ravg = (R1 + R2)/2 = 4.75 mm

a) from the plot, approximate slope of the linear portion = 1/400

B = H

=> = B/H = 1/600

b) H =NI/(2*ravg)

=> H = (30)(0.2)/(2)(3.14)(4.75*10-3)

=> H = 201.14 A/m

B = 0.5 T (from plot)

c) H =NI/(2*ravg)

=> H = (30)(5)/(2)(3.14)(4.75*10-3)

=> H = 5028.5 A/m

B = 1.7 T (from plot)