A hemisphere of radius r is placed in a uniform electric field of strength E. The electric flux through the hemisphere is

$- E \pi r^2$

$\phi=\oint E . d S = \oint {}_A^B E . d S + \oint {}_B^x E . d S + \oint {}_x^A E . d S$

$=-E \pi r^2+E \pi r^2-E \pi r^2=-E \pi r^2$

short cut AXB is symmetrical surface

∴ Electric flux due to this part is zero. However, electric flux due to AB part is –EπR².