The electric field intensity at a point between two parallel sheets with like charges of the same surface charge density $(\sigma)$ is:

The electric field inside a spherical shell of uniform surface charge density is

As shown in the figure,a charged ball $B$ is suspended from a large charged conducting plate by a silk thread $S$ making an angle $\theta$ with the plate. The surface charge density $\sigma$ of the plate is proportional to ........

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?

Two large,thin metal plates are parallel and close to each other. Their inner faces have surface charge densities of the same sign and magnitude $17.7 \times 10^{-22} \ C/m^2$. What is the electric field $E$ in the outer region of the second plate?

$(a)$ Show that the normal component of the electrostatic field has a discontinuity from one side of a charged surface to another given by $(E_2 - E_1) \cdot \hat{n} = \frac{\sigma}{\varepsilon_0}$, where $\hat{n}$ is a unit vector normal to the surface at a point and $\sigma$ is the surface charge density at that point. (The direction of $\hat{n}$ is from side $1$ to side $2$.) Hence, show that just outside a conductor, the electric field is $\frac{\sigma \hat{n}}{\varepsilon_0}$. $(b)$ Show that the tangential component of the electrostatic field is continuous from one side of a charged surface to another.