$A$ positive point charge is released from rest at a distance $r_0$ from a positive line charge with uniform density. The speed $(v)$ of the point charge,as a function of instantaneous distance $r$ from the line charge,is proportional to

$A$ cubical volume is bounded by the surfaces $x = 0, x = a, y = 0, y = a, z = 0, z = a$. The electric field in the region is given by $\overrightarrow{E} = E_0 x \hat{i}$,where $E_0 = 4 \times 10^4 \text{ N C}^{-1} \text{m}^{-1}$. If $a = 2 \text{ cm}$,the charge contained in the cubical volume is $Q \times 10^{-14} \text{ C}$. The value of $Q$ is $...........$ (Take $\varepsilon_0 = 9 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{m}^{-2}$)

Sketch the electric field lines for a uniformly charged hollow cylinder shown in the figure.

The electrostatic field of a long uniformly charged wire varies with distance $r$ according to which relation?

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 $2R$ 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 large thin parallel metal plates have surface charge densities of equal magnitude but opposite signs $(\sigma = 26.4 \times 10^{-12} \ C/m^2)$. The electric field between these plates is ........ $N/C$.