Practice question

**Series combination** of capacitors has same charge Q on each because connected end-to-end, single path for charge flow, induced charges equal, total voltage V = Σ V_i = Q Σ 1/C_i, so 1/C_eq = Σ 1/C_i. Different potential differences V_i = Q/C_i inversely proportional to C_i, smaller C gets larger V. U = -p E cos θ = -4 × 10⁻⁹ × 5 × 10⁴ × cos 30° . cos 30° = (√(3)/2) ≈ 0.866 , so U = -4 × 10⁻⁹ × 5 × 10⁴ × 0.866 = -1.732 × 10⁻⁴ J . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr,