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 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

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

In the absence of other conductors, the surface charge density

A semicircular ring of radius $'a'$ has charge density $\lambda  = {\lambda _0}\,\cos \,\theta $ where ${\lambda _0}$ is constant and $'\theta'$ is shown in figure. Then total charge on the ring is