The electric field in a certain region is acting radially outward and is given by $E = Ar$. $A$ charge contained in a sphere of radius $a$ centered at the origin of the field will be given by:

$A$ 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 $\varepsilon_0 = 9 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{m}^{-2}$)

Obtain the expression for the electric field due to a uniformly charged spherical shell at a point outside it.

If a small sphere of mass $m$ and charge $q$ is hung from a silk thread at an angle $\theta$ with the surface of a vertical charged conducting plate,then for equilibrium of the sphere,the surface charge density of the plate is

Two spherical,nonconducting,and very thin shells of uniformly distributed positive charge $Q$ and radius $d$ are located a distance $10d$ from each other. $A$ positive point charge $q$ is placed inside one of the shells at a distance $d/2$ from the center,on the line connecting the centers of the two shells,as shown in the figure. What is the net force on the charge $q$?

$A$ 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