Mention applications of Gauss’s law.
The applications of Gauss's law are as below :
$(1)$ To obtain field due to an infinitely long straight uniformly charged wire.
$(2)$ To obtain field due to uniformly charged infinite plane sheet.
$(3)$ To obtain field due to uniformly charged thin spherical shell.
$(4)$ To obtain field due to uniformly charged sphere.
The volume charge density of a sphere of radius $6 \,m$ is $2 \,\mu cm ^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is $....\times 10^{10}\, NC ^{-1}$. [Given : Permittivity of vacuum $\left.\epsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1}- m ^{-2}\right]$
A solid ball of radius $R$ has a charge density $\rho $ given by $\rho = {\rho _0}\left( {1 - \frac{r}{R}} \right)$ for $0 \leq r \leq R$. The electric field outside the ball is
Consider a metal sphere of radius $R$ that is cut in two parts along a plane whose minimum distance from the sphere's centre is $h$. Sphere is uniformly charged by a total electric charge $Q$. The minimum force necessary to hold the two parts of the sphere together, is
The electric intensity due to an infinite cylinder of radius $R$ and having charge $q$ per unit length at a distance $r(r > R)$ from its axis is
An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho$. It has a spherical cavity of radius $R / 2$ with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point $P$, which is at a distance $2 \ R$ from the axis of the cylinder, is given by the expression $\frac{23 \rho R }{16 k \varepsilon_0}$. The value of $k$ is