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Question

A uniform field \( E = 5 \times 10^3 \, \text{N/C} \) is along the x-axis. What is the flux through a
circle of radius 20 cm in the yz-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 = π (0.2)² = 0.1256 m² . Flux: Φ = E A cos 0° = 5 × 10³ × 0.1256 = 628 N·m²/C . Substituting values gives 628 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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