Consider a uniform spherical volume charge distribution of radius $R$. Which of the following graphs correctly represents the magnitude of the electric field $E$ at a distance $r$ from the centre of the sphere?

The electric field $\vec E = {E_0}y\hat j$ acts in the space in which a cylinder of radius $r$ and length $l$ is placed with its axis parallel to $y-$ axis. The charge inside the volume of cylinder is 

A hollow metal sphere of radius $R$ is uniformly charged. The electric field due to the sphere at a distance r from the centre

Consider $a$ uniformly charged hemispherical shell of radius $R$ and charge $Q$ . If field at point $A (0, 0, -z_0)$ is $ \vec E$ then field at point $(0, 0, z_0)$ is $[z_0 < R]$ 

The nuclear charge $(\mathrm{Ze})$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho$ (r) [charge per unit volume] is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure The electric field is only along rhe radial direction.

Figure:$Image$

$1.$ The electric field at $\mathrm{r}=\mathrm{R}$ is

$(A)$ independent of a

$(B)$ directly proportional to a

$(C)$ directly proportional to $\mathrm{a}^2$

$(D)$ inversely proportional to a

$2.$ For $a=0$, the value of $d$ (maximum value of $\rho$ as shown in the figure) is

$(A)$ $\frac{3 Z e}{4 \pi R^3}$ $(B)$ $\frac{3 Z e}{\pi R^3}$ $(C)$ $\frac{4 Z e}{3 \pi R^3}$ $(D)$ $\frac{\mathrm{Ze}}{3 \pi \mathrm{R}^3}$

$3.$ The electric field within the nucleus is generally observed to be linearly dependent on $\mathrm{r}$. This implies.

$(A)$ $a=0$ $(B)$ $\mathrm{a}=\frac{\mathrm{R}}{2}$ $(C)$ $a=R$ $(D)$ $a=\frac{2 R}{3}$

Give the answer question $1,2$ and $3.$

The dimensions of an atom are of the order of an Angstrom. Thus there must be large electric fields between the protons and electrons. Why, then is the electrostatic field inside a conductor zero ?