What ensures that the electric field due to a uniformly charged infinite wire decreases as \( 1/r \) instead of \( 1/r^2
**Closed-surface flux** depends solely on net charge inside, not external charges. This principle allows flux calculation without detailed field integration and forms cornerstone for symmetric charge distributions. The cylindrical symmetry of an infinite wire, when analyzed with Gauss’s law, shows the field depends on the radial distance r with a 1/r relationship. This arises because the field spreads over a cylindrical surface, not a spherical one like a point charge. Substituting values gives Cylindrical symmetry, which matches expected magnitude for this electrostatic configuration, confirm
Ref: NCERT > Physics Book > Electric Charges and Fields > Gauss's Theorem and Total Flux