Surface Bound Charge Density | Lecture Note - Edubirdie

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

2024
Views:

119

Pages:

7
Author:

Jabin F.

"# Surface bound charge density ->" "σb = P · n̂" "n̂ = unit vector outward normal" "σb|x=0 = P · (-x̂)" "σb|x=d = P · (x̂)" Main Equations: σb = P · n̂ σb|r=a = (-ε₀) * Φ(r) / (4πε₀a²) σb|r=b = (ε - ε₀) * Φ(r) / (4πε₀b²) Additional Notes: The equations calculate the surface bound charge density at the inner and outer surfaces of the dielectric sphere. The calculations involve the polarization vector (P), the electric potential (Φ), the permittivity of free space (ε₀), and the permittivity of the dielectric (ε). The direction of the surface bound charge density depends on the direction of the polarization vector and the unit normal vector. Main Equations: V = -∫E · dl V_B - V_A = V = -∫(Pxyî + (1/2)(x² + y²)ĵ) · (dxî + dyĵ + dzk̂) V_B - V_A = V = -∫₀¹ Pxy dx - ∫₀¹ P(1/2)(x² + y²) dy V = -P(1/2 + 8/3) V = -(11/3)P ∇²V = -ρ/ε₀ ∇²V = 16x² + f''(x) - 6 = 0 f''(x) = 6 - 16e^(2x) f'(x) = 6x - 8e^(2x) + c f(x) = 3x² - 4e^(2x) + d V(0,0,0) = 4 + f(0) - 0 = 0 f(0) = -4 V(x,y,z) = 3x² - 4e^(2x) - 4

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