Potential Energy of a Magnetic Dipole in a Magnetic Field - Edubirdie

University:
Santa Fe College
Course:
ETS 2527C | Electromechanical Components and Mechanisms
Academic year:

2024
Views:

183

Pages:

5
Author:

Jabin F.

Potential energy of a magnetic dipole in a magnetic field (B) Um = -(m·B) Force Fm = -∇Um = +∇(m·B) this method is quick for force calculation In previous derivations: m = Iabz B = Byz F = ∇(Iabz· Byz) = IabB∇(yz) = IabB[∂y(yz)] = IabBy F = IabBy Torque (in non-Uniform magnetic field) τ = (m x B) + (r x F) τ = (m x B) + [r x ∇(m·B)] 24/3.75 Poyg = -79 E = ER + iεI E = ER + i√3E Where ER = √3 Unit of B ratio → m/g.ee. Unit of (E/H) ratio → Z = wave impedance Z = (E/H) = √(μ/ε) = √(μo/εo)√(μr/εr) = Zo√(μr/εr) Permeability not given μ = μoμr = 1 ε = εoεr Z = Zo/√(εr) tan φ = (KI/KR) = β/α φ = [θE/(2π)] from eqn (i) Er1 = ER + iεI |Er1| = √[(ER)² + (εI)²] |Er1| = EI√[(ER/EI)² + 1] |Er1| = ER√[1 + (EI/ER)²] |Er1| = ER√[1 + 3] = ER√(2) from (iii) z = (120π)/(√α√εR) skin depth δ = λo/4π δ = π/β → β = 4π/λo α = √[β² (4π/λo)] |K|^2 = √[ω² + β²] = (4π/λo)√[1 + 3] = 8π/λo if given: K = ω + iβ = (E/H) = (c/μ) n* = mr + imi tanφ = (mi/mr)

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