EF and PE of Sphere | Santa Fe College - Edubirdie

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

2024
Views:

407

Pages:

3
Author:

Jabin F.

# Calculate the E.F and pot'n inside and outside an uniformly charge sphere of total charge 2 and radius R. also Calculate its potential energy. ρ=uniform Soln: q = ∫ρ dτ = ρ∫ dτ ρ = 3q / 4πR³ = 3q / 4πR³ for r < R: qenc = ∫ρ dτ = ρ∫ 4πr² dr = 3q / 4πR³ * 4π * r³/3 qenc = qr³/R³ Electric field: ∮⃗E · d⃗a = qenc / ε₀ ⃗E * 4πr² = qenc / ε₀ Ein = (qr³/R³) / (4πε₀r²) Ein = qr / 4πε₀R³ Ein = (qr / 4πε₀R³) * r̂ Ein = q / 36πε₀ # r > R qenc = q Eout * 4πr² = q / ε₀ Eout = q / 4πε₀r² # For a spherically symmetric charge distribution: Eout = (ρR³/3ε₀r²) * r̂

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