Question 7.17: A rectangular ring ferromagnetic material has a 16-cm inner ...
A rectangular ring ferromagnetic material has a 16-cm inner diameter a 20-cm outer diameter and 2.5-cm thickness. A coil of 750 turns is wound on the ring. It is found that to produce a flux of 1.25 m Wb, the coil must carry 1 A. Find the following quantities:
(a) mmf (b) magnetic field intensity (c) flux density (d) reluctance (e) permeability (f) relative permeability
(a) mmf, F = 750 × 1 = 750 AT
(b) Mean dia = \frac{16 + 20}{2} 18 cm
Mean ring length, l_{C} =18π = 56.55 cm
Magnetic field intensity H_{C} = \frac{750}{56.55 × 10^{-2}} = 1326 AT/m
(c) Core cross-sectional area
A_{C} = (20 – 16) × 2.5 = 10 cm²
Flux density B_{C} = \frac{1.25 × 10^{-3}}{10 × 10^{-4}} = 1.25 T
(d) Reluctance, R = \frac{F}{\phi} = \frac{750}{1.25 × 10^{-3}} = 600 × 10³
(e) Permeability , μ = \frac{B_{C}}{H_{C}} = \frac{1.25}{1.326} 0.943 × 10^{-3}
(f) Relative permeability, μ_{r} = \frac{μ}{μ_{0}} = \frac{0.943 × 10^{-3}}{4π × 10^{-7}} = 75.04