If $q$ is the charge per unit area on the surface of a conductor,then the electric field intensity at a point on the surface is

Two infinite sheets of uniform charge density $+\sigma$ and $-\sigma$ are parallel to each other as shown in the figure. The electric field is:

Electric field intensity at points in between and outside two thin separated parallel sheets of infinite dimension with like charges of same surface charge density $(\sigma)$ are . . . . . . and . . . . . . respectively.

There is a solid sphere of radius $R$ having uniformly distributed charge throughout it. What is the relation between electric field $E$ and distance $r$ from the centre (where $r < R$)?

$(a)$ 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.

Two parallel infinite line charges with linear charge densities $+\lambda\; C/m$ and $-\lambda\; C/m$ are placed at a distance of $2R$ in free space. What is the electric field mid-way between the two line charges?