Worked example: A uniform field E = 500 N/C (along +x) passes through a rectangular surface 0.2 m × 0.3 m whose normal makes 60° with the field. (a) Find the flux. (b) What if the surface is turned so its normal is perpendicular to the field? Step 1: Area A = 0.06 m². Φ = EA·cosθ = (500)(0.06)(cos60°) = 30 × 0.5 = 15 N·m²/C. Step 2: Positive sign means net field lines cross in the direction of the outward normal. Step 3: If the normal is perpendicular to E (θ = 90°), cosθ = 0, so Φ = 0 — the field skims along the surface and nothing crosses it. Step 4 (closed-surface taste): If this rectangle were one face of a closed box in a uniform field, whatever flux enters one face leaves the opposite face, giving zero total flux — consistent with Gauss's law since no charge is enclosed.