Volume Bound Charge Density | Santa Fe College - Edubirdie

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

2024
Views:

301

Pages:

6
Author:

Jabin F.

Volume bound charge density: ρ_b = -∇ · P Static Dielectric Constant of Conductor: Best dielectric: K = ∞ a < r < b: ρ_b = -∇ · P ρ_b = -ε₀ * (ε_r - 1) * ∇ · P ρ_b = -ε₀ * (ε_r - 1) * q * ∇ · (1/r³) ρ_b = -4πε₀ * (ε_r - 1) * q * (δ³/r³) = 0 a < r < b: ρ_b = -∇ · P ρ_b = -ε₀ * (ε_r - 1) * ∇ · (q/r³) ρ_b = -4π * ε₀ * (ε_r - 1) * q * δ³(r) = 0 Ques 16: All are right. Ques 15: V(r=c) = (1 / (4πε₀)) * ∫((4πσa²) / r) dr from a to b V(r=c) = (σ / ε₀) * (a - b) Ques. 26: V(r, θ, φ) = f(r)cosθ ∇²V = (1/r²) * (∂/∂r) * (r² * ∂V/∂r) + (1/(r²sinθ)) * (∂/∂θ) * (sinθ * ∂V/∂θ) Step 1: ∇²V = (1/r²) * (∂/∂r) * (r² * f'(r)cosθ) + (1/(r²sinθ)) * (∂/∂θ) * (sinθ * f(r)(-sinθ)) ∇²V = (1/r²) * (2rf'(r)cosθ + r²f''(r)cosθ) - (1/r²) * f(r) * (cos²θ - sin²θ) ∇²V = (1/r²) * (r²f''(r) + 2rf'(r) - 2f(r))cosθ ⇒ f''(r)r² + 2rf'(r) - 2f(r) = 0 Option (b): Inside: Vα (1/r) Outside: Vα (1/r²) Monopole: f₀(r) = 1 Vα (1/r) Dipole: p(r₀) = 0 Vα (1/r²) Quadrupole: p₂(r₀) = 0 Vα (1/r³)

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