The electrostatic potential inside a charged spherical ball is given by $\phi = ar^2 + b$,where $r$ is the distance from the centre and $a, b$ are constants. Then the charge density inside the ball is:

Consider an atom with atomic number $Z$ as consisting of a positive point charge at the centre and surrounded by a distribution of negative electricity uniformly distributed within a sphere of radius $R$. The electric field at a point inside the atom at a distance $r$ from the centre is

Consider a thin spherical shell of radius $R$ with its centre at the origin,carrying uniform positive surface charge density. The variation of the magnitude of the electric field $|\vec{E}(r)|$ and the electric potential $V(r)$ with the distance $r$ from the centre,is best represented by which graph?

The line $AA^{\prime}$ lies on a charged infinite conducting plane which is perpendicular to the plane of the paper. The plane has a surface charge density $\sigma$. $B$ is a ball of mass $m$ with a like charge of magnitude $q$. $B$ is connected by a string to a point on the line $AA^{\prime}$. The tangent of the angle $\theta$ formed between the line $AA^{\prime}$ and the string is:

$A$ charge $17.7 \times 10^{-4} \ C$ is distributed uniformly over a large sheet of area $200 \ m^2$. The electric field intensity at a distance $20 \ cm$ from it in air will be $\left[\varepsilon_0=8.85 \times 10^{-12} \ C^2/Nm^2\right]$

The electric field due to an infinitely long thin straight wire with uniform linear charge density of $2.5 \times 10^{-7} \ Cm^{-1}$ at a radial distance of $x$ from the wire is $7.5 \times 10^4 \ NC^{-1}$. Then $x=$ (in $cm$)