The potential (in volts ) of a charge distribution is given by

$V(z)\, = \,30 – 5{z^2}for\,\left| z \right| \le 1\,m$

$V(z)\, = \,35 – 10\,\left| z \right|for\,\left| z \right| \ge 1\,m$

$V(z)$  does not depend on $x$  and  $y.$  If this potential is generated by a constant charge per unit volume $\rho _0$ (in units of $\varepsilon _0$ ) which is spread over a certain region, then choose the correct statement

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

In a certain region of space, variation of potential with distance from origin as we move along $x$-axis is given by $V=8 x^2+2$, where $x$ is the $x$-coordinate of a point in space. The magnitude of electric field at a point $(-4,0)$ is ………. $V / m$

A particle $A$ has charge $+q$ and particle $B$ has charge $+ 4q$ with each of them having the same mass $m$. When allowed to fall from rest through same electrical  potential difference, the ratio of their speed $V_A : V_B$ will be :-

The electric potential $V(x)$ in a region around the origin is given by $V(x) = 4x^2\,volts$ . The electric charge enclosed in a cube of $1\,m$ side with its centre at the origin is (in coulomb)