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Question

A uniform electric field \( E = 4 \times 10^3 \, \text{N/C} \) is along the z-axis. What is the flux
through a square of side 15 cm in the xy-plane?

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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 vector Δ S = (0.15)² = 0.0225 m² along z-axis. Flux: Φ = E · Δ S = 4 × 10³ × 0.0225 = 90 N·m²/C . Substituting values gives 90 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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