To calculate the electric field due to an infinite plane sheet of uniform charge density σ, We choose two different gaussian cylinders as shown in figure (I) & figure (II). The appropriate choice is figure (I) because

Engineering

Physics

Electric Flux and Gauss Law and its Applications

Question

The area vectors at the two ends of S₂ must be in the same direction

Gaussian surface cannot cut the continuous distribution of charge

$q_{enclosed} \neq 2 r l σ$

$for S_{2}, \oint \vec{E} \cdot d \vec{s} \neq E (2 πr l)$

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For S₂, field is not radially outward and same at all points on the curved surface.