Name: Displacement Current Density
Brand: EduBirdie
Rating: 5.0 (31 reviews)

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

2024
Views:

473

Pages:

5
Author:

Jabin F.

Top Section Definition of displacement current density (Jd): Jd = ε₀ * ∂E/∂t For a capacitor plate, E = V/d Substituting E in the Jd equation: Jd = (ε₀ * V₀ * ω / d) * cos(ωt) Bottom Section Given: V = V₀ * sin(ωt) E = V₀ * sin(ωt) / d Jd = -ε₀ * (V₀ / d) * ω * cos(ωt) Poynting vector (S): S = (E x B) / μ₀ Top Section B = (μ₀ * V₀ * ω * R / 2d) * cos(ωt - φ) for r ≤ R B = (μ₀ * V₀ * ω * R² / 2d³) * cos(ωt) for r > R S = (E x B) / μ₀ = (μ₀ * V₀² * ω² * R² / 4d²) * sin²(ωt) Bottom Section Option (a): Maximum value of S Smax = (μ₀ * V₀² * ω² * R²) / (4d²) Option (b): Time-averaged average energy flowing out of capacitor = 0 Option (c): From equation (i), the magnetic field (M.F) is dependent on time. Not correct Option (d): ∇ x B = μ₀ * (Jc + Jd) ∇ x B = (μ₀ * V₀ * ε₀ * ω / d) * sin(ωt) This is independent of r. Option (d) is correct.

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