Find the surface charge density at the intersection of the plane $x = 3 \, m$ and the $x$-axis,given a uniform line charge of $8 \, nC/m$ lying along the $z$-axis in free space.

Charge is distributed within a sphere of radius $R$ with a volume charge density $\rho (r) = \frac{A}{r^2} e^{-2r/a}$,where $A$ and $a$ are constants. If $Q$ is the total charge of this charge distribution,the radius $R$ is:

If volume charge density is $\rho$,then what will be the charge on $\Delta V$ volume?

$A$ disc of radius $R$ is charged on its surface with surface charge density $\sigma = \sigma_0 r^3$. Here $\sigma_0$ is a constant and $r$ is the distance from its centre. The total charge on the disc is:

Two isolated metallic spheres of radii $2 \,cm$ and $4 \,cm$ are given equal charge,then the ratio of charge density on the surfaces of the spheres will be

$A$ solid sphere of radius $R_1$ and volume charge density $\rho = \frac{\rho_0}{r}$ is enclosed by a hollow sphere of radius $R_2$ with negative surface charge density $\sigma$, such that the total charge in the system is zero. $\rho_0$ is a positive constant and $r$ is the distance from the centre of the sphere. The ratio $R_2/R_1$ is