The given figure shows two parallel plates $A$ and $B$ with charge densities $+\sigma$ and $-\sigma$ respectively. The electric intensity will be zero in which region?

An infinite line charge produces a field of $9 \times 10^4 \text{ N/C}$ at a distance of $2 \text{ cm}$. The linear charge density is . . . . . . . $\left(k = 9 \times 10^9 \text{ Nm}^2/\text{C}^2\right)$ (in $\text{ } \mu\text{C/m}$)

$A$ force of $10 \; N$ acts on a charged particle placed between two plates of a charged capacitor. If one plate of the capacitor is removed,then the force acting on that particle will be ...... $N$.

Consider the force $F$ on a charge $q$ due to a uniformly charged spherical shell of radius $R$ carrying charge $Q$ distributed uniformly over it. Which one of the following statements is true for $F$,if $q$ is placed at distance $r$ from the centre of the shell?

$A$ spherically symmetric charge distribution is considered with charge density varying as
$\rho(r)=\begin{cases} \rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text{for } r \leq R \\ 0 & \text{for } r>R \end{cases}$
Where,$r (r < R)$ is the distance from the centre $O$ (as shown in figure). The electric field at point $P$ will be.

$A$ sphere of radius $R$ has a volume charge density $\rho = k r$, where $r$ is the distance from the center of the sphere and $k$ is a constant. The magnitude of the electric field at the surface of the sphere is given by ($\varepsilon_{0} =$ permittivity of free space):