University:
Kentucky State University
Course:
PHY 212 | General Physics II
Academic year:

2020
Views:

378

Pages:

17
Author:

ge1mu2k1rrs

**ch22: Gauss's Law** **Flux of electric field:** Number of electric field lines passing through a unit area. Φ = ∫E.dA = EAcosθ **In general:** Φ = ∫E.dA = ∫E dA cosθ **Ex 23-1 Page 608:** Φ = ? Φ = Φ₁ + Φ₂ + Φ₃ = ∫EdA cos0° + ∫EdA cos180° + ∫EdA cos90° = EA + EA + 0 = 0 **Ex: 23-2 Page 609:** E = 3xi + 4j (Non-uniform electric field) [Image of a cubical box with sides of length 2 m] **Sol:** Φ(front) = ∫E.dA = ∫(3xi + 4j).dA = ∫3xdA = ∫[0,2] 3x dx = 9 Nm²/C Φ(back) = ∫E.dA = ∫(3xi + 4j).dA = ∫-3xdA = ∫[0,2] -3x dx = -9 Nm²/C Φ(top) = ∫E.dA = ∫(3xi + 4j).dA = ∫4dA = ∫[0,2] 4dA = 16 Nm²/C **a < r < b** ∫E.dA = q_inc/ε₀ E(4πr²) = q₁/ε₀ E = 1/(4πε₀) * q₁/r² **b < r < c** Conductor E_inside = 0 q_inc = q_inside = 0 q₁ + q_inner = 0 q_inner = -q₁ q_conductor = -q₁ q_inner + q_outer = -q₁ q_outer = 0 **PB5 Page 6.26** R = 5.6 cm ρ = cr **(a) q_enc?** q_enc = ∫ρdV = ∫(cr)(4πr²)dr = 4πc ∫[0,R] r³dr = 4πc [r⁴/4]₀ᴿ = πcR⁴ = 2.78 * 10⁻¹⁵ C **(b) E = ??** r > R ∫E.dA = q_enc/ε₀ E(4πr²) = q_enc/ε₀ E = 1/(4πε₀) * q_enc/r²