$A$ hollow cylinder has a charge $q$ within it. If $\phi$ is the electric flux in units of $V-m$ associated with the curved surface $B,$ the flux linked with the plane surface $A$ in units of $V-m$ will be

An infinite non-conducting sheet has a surface charge density $\sigma = 0.10 \, \mu C/m^2$ on one side. How far apart are equipotential surfaces whose potentials differ by $50 \, V$?

Two large parallel plates have uniform surface charge densities $+\sigma$ and $-\sigma$. The electric field between the plates is:

$(a)$ 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.

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 the electric field is:

$A$ conducting sphere of radius $0.1 \ m$ has a uniform charge density $1.8 \ \mu C/m^2$ on its surface. The electric field in free space at a radial distance of $0.2 \ m$ from the center of the sphere is $(\varepsilon_0 = \text{permittivity of free space})$