📦 Electric Flux — Φ = E·A, and why the surface's size does not matter

Electric flux counts the field lines crossing a surface. Grow the Gaussian sphere and the flux does not budge; slide the charge outside and the flux drops to exactly zero; tilt the open disc and watch cos θ act on its own.

Walkthrough 1 / 5

Step 1 — a charge q on its own, throwing field out in every direction.

Charge q +2.0 µC

Gaussian radius R 5.0

Charge offset x 0.0

Disc tilt θ 0°

closed surface: Φ = 2.26×10⁵ N m²/C
charge inside · R = 5.0 (Φ unchanged)

flat disc: Φ ∝ cos θ = 1.00
at θ = 90° the field lies IN the disc → Φ = 0

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