Explain by graph how the electric field by thin spherical shell depends on the distance of point from centre.

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?

If the total charge enclosed by a surface is zero, does it imply that the electric field everywhere on the surface is zero ? Conversely, if the electric field everywhere on a surface is zero, does it imply that net charge inside is zero.

A charge $Q$ is uniformly distributed over a large square plate of copper. The electric  field at a point very close to the centre of the plane is $10\, V/m$. If the copper plate is  replaced by a plastic plate of the same geometrical dimensions and carrying the same  charge $Q$ uniformly distributed, then the electric field at the point $P$ will be......$V/m$

A solid metallic sphere has a charge $ + \,3Q$. Concentric with this sphere is a conducting spherical shell having charge $ - Q$. The radius of the sphere is $a$ and that of the spherical shell is $b(b > a)$. What is the electric field at a distance $R(a < R < b)$ from the centre

Let there be a spherically symmetric charge distribution with charge density varying as $\rho (r)=\;\rho _0\left( {\frac{5}{4} - \frac{r}{R}} \right)$, upto $r = R$ ,and $\rho (r) = 0$ for $r > R$ , where $r$ is the distance from the origin. The electric field at a distance $r(r < R)$ from the origin is given by