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Question

A uniform field \( E = 9 \times 10^3 \, \text{N/C} \) is along the x-axis. What is the flux through a
rectangle of 35 cm × 45 cm in the yz-plane?

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Explanation

**Electric flux** through surface measures field lines crossing it, Φ = E·A = E A cosθ for uniform field, unit N·m²/C. For circular area in xy-plane with field along z, θ = 0°, cosθ = 1, so Φ = E·πR² directly, maximum when field normal to surface. Area: A = 0.35 × 0.45 = 0.1575 m² . Flux: Φ = E A cos 0° = 9 × 10³ × 0.1575 = 1417.5 N·m²/C . Substituting values gives 1417.5 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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