Question

A hollow half cylinder surface of radius R and length l is placed in a uniform electric field $\overrightarrow{E}$. Electric field is acting perpendicular on the ABCD. If the flux through the curved surface of the hollow cylindrical surface is $E\times XRl$. Find X?

Answer 1

Flux=$\varphi =\overrightarrow{E}.\overrightarrow{\Delta S}$

Hence, flux =$\varphi =E\times$ projection of area normal to the direction of field so that area vector can be along $\overrightarrow{E}$.

Here, projection of half cylinder perpendicular to field E gives a rectangular area ABCD of area $AB\times AD$

Hence, flux$=\varphi =E\times (2R\times l)$

$⟹\varphi =E\times 2Rl$

Hence, $X=2$