In a region of space,the electric field is given by $\vec E = 8\hat i + 4\hat j + 3\hat k$. The electric flux through a surface of area $100 \text{ units}$ in the $x-y$ plane is...

$A$ charge is kept at the central point $P$ of a cylindrical region. The two edges subtend a half-angle $\theta$ at $P$, as shown in the figure. When $\theta=30^{\circ}$, then the electric flux through the curved surface of the cylinder is $\Phi$. If $\theta=60^{\circ}$, then the electric flux through the curved surface becomes $\Phi / \sqrt{n}$, where the value of $n$ is. . . . . . .

The figure shows some of the electric field lines corresponding to an electric field. The figure suggests

Four charges $2 \mu C, -3 \mu C, 4 \mu C, -4 \mu C$ and $-1 \mu C$ are enclosed by a Gaussian surface of radius $2 \ m$. The net outward flux through the Gaussian surface is (in $\mu V-m$):

$A$ sphere of radius $R$ has a charge $Q$. $A$ concentric spherical Gaussian surface of radius $2R$ is drawn. The electric flux associated with the Gaussian surface is ........

If the charges inside a sphere are $+2 \times 10^{-6} \ C$,$-5 \times 10^{-6} \ C$,$-3 \times 10^{-6} \ C$,and $+6 \times 10^{-6} \ C$,what is the total electric flux passing through the sphere?