Gauss's Applications PDF
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This document discusses Gauss's applications in calculating electric fields at certain points. It covers various scenarios, including point charges, line charges, sheets of charge, and conducting/non-conducting spheres. It also delves into electric flux calculations. Formulas related to these concepts are included and demonstrated.
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# Gauss's Applications “Calculate E at certain point" * 9 * 10⁹ K = 1/4πε₀ = N m² / C² * 8.85 * 10⁻¹² C² / N m² ### Source of E - Point charge - E = kQ/r² - E = Q/(4πε₀r²) - r: definition of distance from *Q* to the point - Line charge - E = 2kλ/r - E = λ/(2πε₀r) - r: perpendicular di...
# Gauss's Applications “Calculate E at certain point" * 9 * 10⁹ K = 1/4πε₀ = N m² / C² * 8.85 * 10⁻¹² C² / N m² ### Source of E - Point charge - E = kQ/r² - E = Q/(4πε₀r²) - r: definition of distance from *Q* to the point - Line charge - E = 2kλ/r - E = λ/(2πε₀r) - r: perpendicular distance from line to the point - Sheet of charge - E = σ/(2ε₀) - E = 2πkσ - r: perpendicular distance from sheet to the point - Conducting sphere - E(inside) = 0 - E(out) = kQ/r² - E(out) = Q/(4πε₀r²) - r: distance from center to the point - Non-conducting sphere - E(inside) = kQr/(4πε₀R³) - E(inside) = σr/(3ε₀) - E(in) = kσr/R³ - E(in) = σr/(4πε₀R³ ) - E(out) = kQ/r² - E(out) = Q/(4πε₀r²) - E(out) = kσR³/(3ε₀r²) - E(out) = σR³/(3πε₀r²) # Electric Flux ### Rule * φ = E•A = E•A cos(θ) * A: magnitude of area (m²) * â: normal unit vector * ǹ: normal vector * n: magnitude of normal vector ### Notes - φ(total) = ∑ φ(face), “total Flux” - φ(net) = φ(total) – E₀ - φ(net) = Σ Q(enc), “total charge” - φ(total) = Σ φ(enc), “total flux” - φ(enc) = q₁ + q₂ + q₃
