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Question
A charge q is placed at the centre of the open end of a cylindrical vessel (see the figure). The flux of the electric field through the surface of the vessel is ____________ .
Options
zero
q/εv
q/2εv
2q/εv
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Solution
q/2ε0
According to Gauss's Law, the flux through a closed cylindrical Gaussian surface is q/ε0. But the question is about an open cylindrical vessel. Now, take another identical vessel and make a closed Gaussian surface enclosing the charge, as shown in the following figure.
Total flux linked with the closed Gaussian surface,
Ø T =`q/ε_0`
Flux linked with the surface of a open ended cylindrical vessel,
Ø = `(Ø"T")/2 = q/(2ε_0)`
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