A conducting sphere of radius $10 \;cm$ has an unknown charge. If the electric field $20\; cm$ from the centre of the sphere is $1.5 \times 10^{3} \;N / C$ and points radially inward, what is the net charge (in $n\;C$) on the sphere?

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 

The dimensions of an atom are of the order of an Angstrom. Thus there must be large electric fields between the protons and electrons. Why, then is the electrostatic field inside a conductor zero ?

An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho$. It has a spherical cavity of radius $R / 2$ with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point $P$, which is at a distance $2 \ R$ from the axis of the cylinder, is given by the expression $\frac{23 \rho R }{16 k \varepsilon_0}$. The value of $k$ is

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

Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho_0r^2$  ($\rho_0$  is a constant and r is measure from centre).Consider two points $A$ and $B$ at distance $x$ and $y$ respectively ($x < R, y > R$) from the centre. If magnitudes of electric fields at points $A$ and $B$ are equal, then