A Charge q is placed at the centre of the open end of...

A Charge $q$ is placed at the centre of the open end of cylindrical vessel. The flux of the electric field through the surface of the vessel is $\ldots \ldots \ldots \ldots$
(A) $\left(\mathrm{q} / \in_{0}\right)$
(B) (q / $2 \in_{0}$ )
(C) $\left(2 q / \epsilon_{0}\right)$
(D) Zero

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Key Concepts

Closed versus Open Surfaces

Understanding the distinction between closed and open surfaces is critical in applying Gauss's Law. A closed surface completely encloses a volume, allowing the total flux to be directly related to the enclosed charge. In contrast, an open surface does not fully enclose a region, meaning the flux through it cannot be simply linked to enclosed charge without additional considerations about the field's geometry and distribution.

Gauss's Law

Gauss's Law states that the net electric flux through a closed surface is equal to the total charge enclosed divided by the permittivity of free space (??). This principle is a cornerstone of electromagnetism, providing a method to calculate electric fields when symmetry is present, but it strictly applies only to closed surfaces where the entire charge is enclosed.

Electric Flux

Electric flux is a measure of the number of electric field lines passing through a given surface. It quantifies the flow of the electric field through a surface and is defined mathematically as the surface integral of the electric field over that area. The concept is necessary to understand how field lines interact with different surfaces.

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