Question 7.15: A toroid is composed of three parts of different materials b...
A toroid is composed of three parts of different materials but of uniform cross-sectional area. Their mean length and relative permeability are:
I_{1} = 0.15 m, μ_{r1} = 1447 (cast steel)
I_{2} = 0.30 m, μ_{r2} = 5969 (mild silicon steel)
I_{3} = 0.45 m, μ_{r3} = 47750 (nickel iron)
It is required to establish a flux of 0.6 m Wb in the toroid. Calculate.
(a) the magnetic field intensity in each part
(b) the mmf required
(c) the excitation current of the coil
(a) Flux density B = \frac{\phi }{A} = \frac{0.6 × 10^{-3}}{0.001} = 0.6T uniform in all the parts A 0.001 Magnetic field intensities
H_{1} = \frac{B}{μ_{0} μ_{r1}} = \frac{0.6}{4π × 10^{-7} × 1447} = 330 AT/m
H_{2} = \frac{B}{μ_{0} μ_{r2}} = \frac{0.6}{4π × 10^{-7} × 5969} = 80 AT/m
H_{3} = \frac{B}{μ_{0} μ_{r3}} = \frac{0.6}{4π × 10^{-7} × 47750} = 10 AT/m
(b) F = H_{1} l_{1} + H_{2} l_{2} + H_{3} l_{3}
= 330 × 0.15 + 80 × 0.30 + 10 × 0.45 = 78 AT
(c) Excitation current
I = \frac{F}{N} = \frac{78}{100} = 0.78 A