Practice question

**Relation E = -∇V** shows field points down potential gradient. For system of opposite charges close together, equipotential near midpoint between them has V≈0, but shape distorted, not spherical, reflecting superposition of potentials V = k q₁/r₁ + k q₂/r₂. U = -p E cos θ = -8 × 10⁻⁹ × 1 × 10⁵ × cos 60° . cos 60° = 0.5 , so U = -8 × 10⁻⁹ × 1 × 10⁵ × 0.5 = -4 × 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