$A$ solid metallic sphere has a charge $+3Q$. Concentric with this sphere is a conducting spherical shell having charge $-Q$. The radius of the sphere is $a$ and that of the spherical shell is $b$ $(b > a)$. What is the electric field at a distance $R$ $(a < R < b)$ from the center?

$A$ non-conducting solid sphere of radius $R$ has a uniform volume charge density $\rho$. The electric potential at the center of the sphere is related to the potential at the surface and outside the sphere due to this uniform charge distribution.
Statement-$1$: When a charge $q$ is moved from the surface to the center of the sphere,the change in its potential energy is $q\rho R^2 / 6\varepsilon_0$.
Statement-$2$: The electric field at a distance $r$ $(r < R)$ from the center of the sphere is $\rho r / 3\varepsilon_0$.

The electrostatic potential inside a charged spherical ball is given by $\Phi = a r^2 + b$,where $r$ is the distance from the centre and $a, b$ are constants. Then,the charge density inside the ball is ($\varepsilon_0 =$ permittivity in free space).

Explain by graph how the electric field by a thin spherical shell depends on the distance of a point from the centre.

Two parallel large thin metal sheets have equal surface charge densities $(\sigma = 26.4 \times 10^{-12} \, C/m^2)$ of opposite signs. The electric field between these sheets is

Let $\rho (r) = \frac{Q}{\pi R^4} r$ be the volume charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $p$ inside the sphere at distance $r_1$ from the centre of the sphere,the magnitude of the electric field is: