A hemispherical body is placed in a uniform electric field E. What is the flux linked with curved surface, if field is perpendicular to base in figure.
 

Let us consider that the given hemispherical body as a closed surface (whose flux is $\mathrm{\varphi }$₂ ) In this case, the electric flux linked with the body is zero since the body does not enclose any charges:
$\mathrm{\varphi }={\mathrm{\varphi }}_1+{\mathrm{\varphi }}_2=0$
$\Rightarrow {\mathrm{\varphi }}_1=-{\mathrm{\varphi }}_2$………………(1)
Since the field acts perpendicular to the base, the flux linked with the base is given by
${\mathrm{\varphi }}_2=\mathrm{E}\times {\mathrm{\pi R}}^2\cos {180}^{\circ }=-{\mathrm{\pi R}}^2\mathrm{E}$
Therefore, the flux linked with the curved surface is
$\Rightarrow {\mathrm{\varphi }}_1=-{\mathrm{\varphi }}_2=-\left(-{\mathrm{\pi R}}^2\mathrm{E}\right)={\mathrm{\pi R}}^2\mathrm{E}$