Question

A charge Q is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and Gauss's Law, find the flux of the electric field due to this charge through the surface of the hemisphere (figure 30-E3).

Answer 1

From Guass's law, flux through a closed surface,

$\varphi =\frac{Q_{\mathrm{en}}}{{\in }_0}$,
where
Q_en = charge enclosed by the closed surface
Let us assume that a spherical closed surface in which the charge is enclosed is Q.
The flux through the sphere,
$\varphi =\frac{Q}{{\mathit{\in }}_0}$



Hence for a hemisphere(open bowl), total flux through its curved surface,

$\varphi \text{'}=\frac{Q}{{\in }_0}\times \frac{1}{2}=\frac{Q}{2{\in }_0}$