Electric Charges & Fields
Class 12 · Electric Charges & Fields

Gaussian Surface — Cylinder

Closed Gaussian cylinder around a line charge. E = λ/(2πε₀r).

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Key Notes

01

Use a cylindrical Gaussian surface coaxial with a long line charge.

02

Flux through curved side = E·2πrL; flux through end caps = 0 (E ⟂ caps).

03

Result: E = λ/(2πε₀r), perpendicular to wire.

Formulas

Line-charge field

From Gauss law on cylinder.

Important Points

Works for any cylindrical symmetry (charged rod, hollow cylinder, etc.).

Key trick: pick Gaussian surface to align with field symmetry.

Gaussian Surface — Cylinder notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.