Question

The electric flux passing through a hemispherical surface of radius R placed in an electric field E with its axis parallel to the filed is :

• A. $\pi R^{2}E$
• B. $2\pi R^{2}E$
• C. $2\pi RE$
• D. $2\pi R^{3}E$

Answer 1

The correct option is A $\pi R^{2}E$

Electric flux through a hemispherical surface radius $=R$

electric field $=E$

$\int d\left(A\cos \theta \right)=\pi R^2$

$\varphi =\int Ed\left(A\cos \theta \right)$

$=E\int d\left(A\cos \theta \right)$

$=\pi R^{2}E$