question_answer

A cylinder of radius r and length I 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)  \[\left( \pi {{r}^{2}}+\pi {{l}^{2}} \right)E\]

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 \[\Delta \phi =\overset{\to }{\mathop{E}}\,,\Delta \overset{\to }{\mathop{S}}\,\] \[=E\Delta S\cos {{90}^{o}}\] Summing over die entire surface, the total flux from the surface of cylinder is zero.