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Question

A uniform field \( E = 8 \times 10^3 \, \text{N/C} \) is along the y-axis. What is the flux through a
circle of radius 15 cm in the xz-plane at 30° to the y-axis?

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Explanation

**Measure of field penetration** depends on both magnitude and projected area. Understanding angle between E and normal vector is crucial, flux zero when field parallel to surface, maximum when perpendicular. Area: A = π (0.15)² = 0.0707 m² . Flux: Φ = E A cos 30° = 8 × 10³ × 0.0707 × (√(3)/2) = 489.7 N·m²/C . Substituting values gives 490 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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