The electrostatic potential inside a charged spherical ball is given by $\varphi =a{r}^2+b$, where $r$ is the distance from the centre, $\mathrm{a}, \mathrm{b}$ are constants. Then the charge density inside the ball is

This questions has Statement $1$ and Statement $2.$ Of the four choices given after the statements, choose the one that best describes the two statements.

An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho .$ As a result of this uniform charge distribution there is a finite value of the electric potential at the centre of the sphere, at the surface of the sphere and also at a point outside the sphere. The electric potential at infinity is zero.

Statement $1$: When a charge is taken from the centre to the surface of the sphere its potential energy changes by $\frac{q\rho }{3{\epsilon }_0}$
Statement $2$: The electric field at a distance $r(r<R)$ from the centre of the sphere is $\frac{\rho r}{3{\epsilon }_0}$

A charge $Q$ is uniformly distributed over a long rod $AB$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at distance $L$ from the  end $A$ is

Assume that an electric field  $\overrightarrow{\mathrm{E}}=30{\mathrm{x}}^2\hat{\mathrm{i}}$ exists in space. Then find the potential difference  ${\mathrm{V}}_{\mathrm{A}}-{\mathrm{V}}_0,$ where ${\mathrm{V}}_0$ is the potential at the origin and  ${\mathrm{V}}_{\mathrm{A}}$ the potential at $\mathrm{x}=2 \mathrm{m}$ is