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

In a certain region of space, the potential is given by : $V = k[2x^2 - y^2 + z^2].$ The electric field at the point $(1, 1, 1) $ has magnitude =

A sphere carrying charge of $Q$ having weight $w$ falls under gravity between a pair of vertical plates at a distance of $d$ from each other. When a potential difference $V$ is applied between the plates the acceleration of sphere changes as shown in the figure, to along line $BC$. The value of $Q$ is :-

The electric potential at a point $(x, y, z)$ is given by $V=-x^2y-xz^3 +4 $. The electric field at that point is  

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

Figure shows three points $A$, $B$ and $C$ in a region of uniform electric field $\overrightarrow E $. The line $AB$ is perpendicular and $BC$ is parallel to the field lines. Then which of the following holds good. Where ${V_A} > {V_B}$ and ${V_C}$ represent the electric potential at points $A$, $B$ and $C$ respectively