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

2024
Views:

247

Pages:

5
Author:

Jabin F.

Dielectric: A perfect insulating material with the additional property of polarization. Electric field in air: E₀ Net field in the presence of a dielectric: E₁ < E₀ Relationship between E₁ and E₀: E₁ = E₀ / K K: Dielectric constant Polarization: Vector quantity (P) Non-zero if dipoles are not randomly oriented. Diagram: Shows a parallel-plate capacitor with air and then a dielectric inserted. Illustrates the electric field (E₀) in air and the reduced electric field (E₁) in the presence of the dielectric. Represents the polarization vector (P) within the dielectric material. Problem: Question 9 Page 9 Calculations: Inside the cylinder: E_in = K * E₀ ∫ E * ds = 2πKL * ∫₀³ r dr dz ∫ E * ds = 2πKL * (3/2) * L³ E_in = 3πKL³ / (2ε₀) Outside the cylinder: ∫ E * ds = 2πKL * ∫₃ᴿ r dr dz ∫ E * ds = 2πKL * (1/2) * (R² - 9) E_out = KR³ / (2ε₀) For Cylinder: φ = K * ρ * α * s^n E_in ∝ s^(n+1) E_out ∝ 1/s Calculations: E_net = E_+ + E_- E = ρ * r^2 / (3ε₀) E = ρ * (r - r_-) / (3ε₀) E_net = ρ * d / (3ε₀) Calculations: E = -∇V E = - (8x^2 + 2(y-2)^2 + 2zk) E = 4y (c) ✓ V = ∫ E_out dr - ∫ E_in dr Question 11 Page 12 Calculations: V = λR / (2ε₀(R² + z²)^(1/2)) V₁/V₂ = (r² + 9r²)^(1/2) / (r² + 4r²)^(1/2) V₁/V₂ = √10 / √5 V₁/V₂ = √2