Gauss's law can help in the easy calculation of the electric field due to:

An electrostatic field in a region is radially outward with magnitude $E = \alpha r$,where $\alpha$ is a constant and $r$ is the radial distance. The charge contained in a sphere of radius $R$ in this region (centered at the origin) is:

The potential due to an electrostatic charge distribution is $V(r) = \frac{q e^{-\alpha r}}{4 \pi \varepsilon_{0} r}$,where $\alpha$ is positive. The net charge within a sphere centred at the origin and of radius $1/\alpha$ is

The electric field due to a uniformly charged sphere of radius $R$ as a function of the distance $r$ from its centre is represented graphically by

$A$ positive point charge is released from rest at a distance $r_0$ from a positive line charge with uniform density. The speed $(v)$ of the point charge,as a function of instantaneous distance $r$ from the line charge,is proportional to

An infinitely long thin straight wire has a uniform linear charge density of $\frac{1}{3} \text{ C m}^{-1}$. The magnitude of the force acting on a charge of $3 \mu\text{C}$ situated at a point $18 \text{ cm}$ away from the wire is:
$\left(\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ N m}^2 \text{ C}^{-2}\right)$