Inductance: Solid Cylindrical Conductor PDF
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This document provides a detailed analysis of the calculation of inductance for a solid cylindrical conductor, including formulas for and steps to finding magnetic field intensity, magnetic flux density, and flux linkages. Useful for undergraduate engineering students.
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Module 4 Chapter 4.4 Inductance: Solid Cylindrical Conductor All Rights Reserved 1 Inductance: Solid Cylindrical Conductor The inductance of a magnetic circuit that has a constant permeability µ can be obtained by determining the following: 1. 2. 3. 4. H - Magnetic field intensity H, from Ampere’...
Module 4 Chapter 4.4 Inductance: Solid Cylindrical Conductor All Rights Reserved 1 Inductance: Solid Cylindrical Conductor The inductance of a magnetic circuit that has a constant permeability µ can be obtained by determining the following: 1. 2. 3. 4. H - Magnetic field intensity H, from Ampere’s law B - Magnetic flux density B (B = µH) λ - Flux linkages λ L - Inductance from flux linkages per ampere (L = λ / I ) 2 Inductance: Solid Cylindrical Conductor 1. H - Magnetic field intensity H, from Ampere’s law x r 3 Inductance: Solid Cylindrical Conductor 2. B - Magnetic flux density B = µH Where: H - Magnetic field intensity µ - permeability µ = µ0 µr µ0 - permeability of free space = 4π x 10-7 H/m µr - relative permeability = 1 for air, 1000 for magnetic materials Units of B: T – Tesla or G – Gauss, or Wb/m2, 1T = 104 G 4 Inductance: Solid Cylindrical Conductor B - Magnetic flux density The differential flux dΦ per-unit length of conductor in the cross-hatched rectangle of width dx shown in figure: If B is uniform 1 to A, then: ф = B A Reluctance (ℛ ): ℛ = Ni/ф Electrical Circuit Magnetic Circuit V Ni R ℛ i ф 5 Inductance 3. Flux linkages λ: Flux linkage inside the conductor 6 Inductance 4. Inductance from flux linkages per ampere (L = λ / I ): Internal inductance per-unit length of conductor due to above flux linkage • The total flux λP linking the conductor out to external point at distance D is the sum of the internal flux linkage, (4.4.9), and the external flux linkage, (4.4.16) from D1 = r to D2 = D. That is: 7 Inductance • Inductance from flux linkages per ampere (L = λ / I ): 8 Inductance • Outside the conductor: Magnetic field 9 Inductance • Outside the conductor: Magnetic field 10
