Practice question

**System of charges** potential energy is sum over pairs U = Σ k q_i q_j/r_ij, work required to assemble charges from infinity. For 28 μC and -14 μC, 0.28 m apart, U=9×10⁹×28×(-14)×10⁻¹²/0.28= -12.6 J, negative indicates bound system. U = -p E cos θ = -6 × 10⁻⁹ × 2 × 10⁵ × cos 45° . cos 45° = (1/√(2)) ≈ 0.707 , so U = -6 × 10⁻⁹ × 2 × 10⁵ × 0.707 = -8.48 × 10⁻⁴ J . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq series, C_eq = ΣC parallel, U = ½ C