question_answer

A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by:

A) \[2\pi {{R}^{2}}E\]                 

B) \[\frac{{{R}^{2}}}{E}\]

C) \[\frac{\pi {{R}^{2}}}{E}\]                  

D) zero

Correct Answer: D

Solution :

(d) zero Flux through surface A, \[{{\phi }_{A}}=E\times \pi {{R}^{2}}\] Flux through surface B, \[{{\phi }_{B}}=-E\times \pi {{R}^{2}}\] Flux  through   curved surface, \[C=\int{E\,.\,ds}\] \[\int{E\,ds\,\cos \,90{}^\circ =0}\] \[\therefore \] Total flux through cylinder \[={{\phi }_{A}}+{{\phi }_{B}}+{{\phi }_{C}}=0\]