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Question

A uniform field \( E = 4 \times 10^3 \, \text{N/C} \) is along the z-axis. What is the flux through a
rectangle of 30 cm × 20 cm in the xy-plane?

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Explanation

**Flux definition** Φ = ∮ E·dA links field to area orientation. For uniform E perpendicular to surface, Φ = E A, with A = πr² for circle. Inclination reduces flux by cosθ factor, sign indicating outward or inward crossing. Area: A = 0.3 × 0.2 = 0.06 m² . Flux: Φ = E A cos 0° = 4 × 10³ × 0.06 = 240 N·m²/C . Substituting values gives 240 N·m²/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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