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

For a charged spherical ball, electrostatic potential inside the ball varies with $r$ as $V =2 ar ^2+ b$. Here, $a$ and $b$ are constant and $r$ is the distance from the center. The volume charge density inside the ball is $-\lambda a \varepsilon$. The value of $\lambda$ is $...........$. $\varepsilon=$ permittivity of medium.

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

A charge $3$ coulomb experiences a force $3000$ $N$ when placed in a uniform electric field. The potential difference between two points separated by a distance of $1$ $cm$ along the field lines is.....$V$

In a region, the potential is represented by $V(x, y, z) = 6x - 8xy - 8y + 6yz$, where $V$ is in volts and $x, y, z$ are in metres. The electric force experienced by a charge of $2$ coulomb situated at point $( 1, 1, 1)$ is