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

2024
Views:

74

Pages:

6
Author:

Jabin F.

# Oscillating electric dipole: Static dipole: A dipole with charges that are fixed in position. Oscillating dipole: A dipole with charges that oscillate. Equation 1: q(t) = q₀cos(ωt) Equation 2: p(t) = q(t)dż = 2q₀dcos(ωt)ż Equivalent problem: If a point charge is performing simple harmonic motion (SHM), z(t) = Asin(ωt), the equivalent dipole moment is p(t) = Pocos(ωt)ż. Dipole Moment: p(t) = 2q₀z(t) p(t) = P₀sin(ωt) Equations (2) and (3) are equivalent. sin(ωt) and cos(ωt) are in phase. Electric Fields: There are three types of fields: Static (Es), Velocity (Ev), and Acceleration (Ea). For a point charge: Es ∝ 1/r² Ev ∝ 1/r² Ea ∝ 1/r Magnetic Fields: For a point charge: Bs = 0 Bv ∝ 1/r² Ba ∝ 1/r Poynting Vector (S): S = (E x B) / μ₀ Sv = 0 Sv ∝ 1/r⁴ Sa ∝ 1/r² Generalized Formulae: V(r,t), A(r,t), E(r,t), B(r,t), S(r,t) Scalar Potential: V(r,t) = 1/(4πε₀) * (p(t)⋅r̂ / r) Dipole Moment: p(t) = P₀cos(ωt)ż p'(t) = -P₀ωsin(ωt)ż Retarded Time: tᵣ = t - r/c Scalar Potential (Continued): V(r,t) = -μ₀P₀ω/(4πrc) * sin(ωt - ωr/c) Vector Potential: A(r,t) = (1/c) * ∫[d/dt' * (p(t') / r')] dt' A(r,t) = -μ₀P₀ω/(4πrc²) * sin(ωt - ωr/c)ż