$A$ 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 centre?

Find the electric field due to an infinitely long charged cylinder of radius $R$ having a linear charge density $\lambda$ at a distance of $R/2$ from its axis.

At a point $20\, cm$ from the centre of a uniformly charged dielectric sphere of radius $10\, cm$, the electric field is $100\, V/m$. The electric field at $3\, cm$ from the centre of the sphere will be.......$V/m$.

In the figure,the inner (shaded) region $A$ represents a sphere of radius $r_A=1$,within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_A=k r$,where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$,the electrostatic charge density varies as $\rho_B=\frac{2 k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their $SI$ units. Which of the following statement$(s)$ is(are) correct?

Consider a sphere of radius $R$ which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2}$ is carved out of it,as shown,the ratio $\frac{|\overrightarrow{E}_{A}|}{|\overrightarrow{E}_{B}|}$ of the magnitude of the electric field $\overrightarrow{E}_{A}$ and $\overrightarrow{E}_{B}$ respectively,at points $A$ and $B$ due to the remaining portion is

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).