Two concentric shells of radii $R$ and $3R$ are placed as shown in the figure. The outer shell carries a charge $Q$. The inner shell is grounded. Find the electric field at point $P$,which is at a distance $2R$ from the center.

An electron revolves around an infinite cylindrical wire having a uniform linear charge density of $2 \times 10^{-8} \, C \cdot m^{-1}$ in a circular path under the influence of an attractive electrostatic field,as shown in the figure. The velocity of the electron with which it is revolving is $......... \times 10^6 \, m \cdot s^{-1}$. (Given: mass of electron $= 9 \times 10^{-31} \, kg$)

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

As shown in the figure,a charged ball $B$ is suspended from a large charged conducting plate by a silk thread $S$ making an angle $\theta$ with the plate. The surface charge density $\sigma$ of the plate is proportional to ........

As shown in the figure,a cuboid lies in a region with an electric field $\vec{E} = 2x^2 \hat{i} - 4y \hat{j} + 6 \hat{k} \; N/C$. The magnitude of the charge within the cuboid is $n \varepsilon_0 \; C$. The value of $n$ is $............$ (if the dimensions of the cuboid are $1 \times 2 \times 3 \; m^3$)

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?