If an insulated non-conducting sphere of radius $R$ has charge density $\rho $. The electric field at a distance $r$ from the centre of sphere $(r < R)$ will be

A hollow insulated conducting sphere is given a positive charge of $10\,\mu \,C$. ........$\mu \,C{m^{ - 2}}$ will be the electric field at the centre of the sphere if its radius is $2$ meters

Two infinitely long parallel wires having linear charge densities ${\lambda _1}$ and ${\lambda _2}$ respectively are placed at a distance of $R$ metres. The force per unit length on either wire will be $\left( {K = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$

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?

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

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude $17.0\times 10^{-22}\; C/m^2$. What is $E$:

$(a)$ in the outer region of the first plate,

$(b)$ in the outer region of the second plate, and

$(c)$ between the plates?