question_answer

A cylinder of radius r and length \[l\] is placed in an uniform electric field E parallel to the axis of the cylinder. The total flux for the surface of the cylinder is given by:

A)  zero                                     

B)  \[2\pi {{r}^{2}}E\]

C)  \[\pi {{r}^{2}}E\]                             

D)  \[(\pi {{r}^{2}}+\pi {{l}^{2}})\,E\]

Correct Answer: A

Solution :

Let us take a small area \[\Delta S\] on the cylindrical surface. The normal to this area will be perpendicular to the axis of the cylinder and electric field is parallel to axis of cylinder. So, flux \[\Delta \,\phi =\vec{E}\,.\,\Delta \,\vec{S}\]                                 \[=E\,\Delta \,S\cos {{90}^{o}}\]                                 = 0 Summing over the entire surface, the total flux from the surface of cylinder is zero.