Power Radiated By an Accelerated Point Charge - Edubirdie

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

2024
Views:

93

Pages:

5
Author:

Jabin F.

# Power radiated by an accelerated Point charge (2): Larmor generalised power radiated P = (2/3) * (q²a²/6πε₀c³) * [a² - (v²a²/c²)] Limiting Case → 1. If v̂ and â are parallel (θ = 0°) If charge particle is travelling along a straight line. a ≠ 0, v ≠ 0 → P = (2/3) * (q²a²/6πε₀c³) * a² → Bremsstrahlung radiation or Braking radiation. here v = √(1 - v²/c²) This type of radiation produces when highly energetic electrons hit the metal target in X-Ray tube. 2. When v̂ and â are ⊥ (θ = 90°) # charge in circular motion: P = (μ₀q²γ⁶ / 6πc) * [a² - (v²a²/c²)] = (μ₀q²γ⁶a² / 6πc) * [1 - (v²/c²)] = (μ₀q²r⁴a² / 6πc) * (1 / γ²) = (μ₀q²r⁴a² / 6πc) * (1 / (1 - v²/c²)) → Synchrotron radiation 3. If charge is moving non-relativistically (v << c): v ≈ 1 either θ = 0° or θ = 90° P = μ₀q²a² / 6πc = q²a² / 6πε₀c³ = (1 / ε₀c²) * (q²a² / 6πc) = (μ₀ / ε₀c²) * (q²a² / 6πc) = (1 / c²) * (q²a² / 6πc) = q²a² / 6πc³ Gaussian Units ε₀ = 1 / 4π P = (q²a²/6πc³) * 4π P = (2/3) * (q²a²/c³)

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