Calculating Self-Energy in Electrostatics | Santa Fe College - Edubirdie

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

2024
Views:

481

Pages:

2
Author:

Jabin F.

# Energy U = (Ɛ₀ / 2) ∫(E² * dτ) U = (Ɛ₀ / 2) ∫₀ᴿ (E_in² * 4πr²dr) + (Ɛ₀ / 2) ∫ᴿ∞ (E_out² * 4πr²dr) U = (Ɛ₀ / 2) ∫₀ᴿ (2r / 4πε₀R³) * 4πr²dr + (Ɛ₀ / 2) ∫ᴿ∞ (9 / 4πε₀²r⁴) * 4πr²dr U = (Ɛ₀q² / 8πε₀R³) ∫₀ᴿ r⁴dr + (Ɛ₀q² / 8πε₀²) ∫ᴿ∞ r⁻²dr U = (Ɛ₀q² / 8πε₀R³) [r⁵ / 5]₀ᴿ + (Ɛ₀q² / 8πε₀²) [-1/r]ᴿ∞ U = (2q² / 8πε₀R) [(1/5) - 1] U = (2q² / 8πε₀R) (6/5)

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