Consider $a$ uniformly charged hemispherical shell of radius $R$ and charge $Q$ . If field at point $A (0, 0, -z_0)$ is $ \vec E$ then field at point $(0, 0, z_0)$ is $[z_0 < R]$ 

The electric field at a distance $\frac{3R}{2}$ from the centre of a charged conducting spherical shell of radius $R$ is $E.$ The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is 

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.......$V/m$

The electric intensity due to an infinite cylinder of radius $R$ and having charge $q$ per unit length at a distance $r(r > R)$ from its axis is

Let $\rho (r) =\frac{Q}{{\pi {R^4}}}r$ be the 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 electric field is

$(a)$ Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by

$\left( E _{2}- E _{1}\right) \cdot \hat{ n }=\frac{\sigma}{\varepsilon_{0}}$

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 $\sigma \hat{ n } / \varepsilon_{0}$

$(b)$ Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another.