Transformation of Electrodynamics Under STR - Edubirdie

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

2024
Views:

128

Pages:

6
Author:

Jabin F.

# Transformation of electrodynamics Under STR: Z S' 0 # S and S' are two inertial frames of reference. (non-accelerated) for example: S is at rest S' is moving at constant velocity along x, y, or z direction # If we transform from S → S', the following parameters remain unchanged. (Lorentz invariant quantity) 1. Ē⋅Ḃ: Ē'⋅Ḃ' = Ē⋅Ḃ 2. Ē² - c²B²: (Ē')² - c²(Ḃ')² = Ē² - c²B² Energy density of electronic fields: Ue = (1/2)ε₀E² Um = B² / (2μ₀) ⇒ (1/2)ε₀E² - (B²/2μ₀) = (ε₀/2)(E² - B²/μ₀) = (ε₀/2)(E² - c²B²) Relativistically invariant In Gaussian Units: Ē² - B² B → B/c 3. Total charge of any system (q): (S) → (S') q' = q Ques.2 Page-98 ρ(r,t) = 0 ∇⋅E = ρ/ε₀ = 0 E = -∇V ∇²V = 0 ∇²V = (1/r²)(∂/∂r)(r²∂V/∂r) = 0 ⇒ V(r) = A/r + B ⇒ E = -∇V = (A/r²)r̂ ⇒ ρ = ε₀(∇⋅E) = 0 ⇒ Charge distribution: ρ = 0 ⇒ The charge is placed at r = 0 position. ∇×B = μ₀J + μ₀ε₀(∂E/∂t) = 0 ⇒ J = 0 (since E is not time-dependent)

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