The potential gradient is a

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:

A cathode ray tube contains a pair of parallel metal plates $1.0\, cm$ apart and $3.0\, cm$ long. A narrow horizontal beam of electron with a velocity $3 \times 10^7\, m/s$ passed down the tube midway between the plates. When a potential difference of $550\, V$ is maintained across the plates, it is found that the electron beam is so deflected that it just strikes the end of one of the plates. Then the specific charge of the electron in $C/kg$ is

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

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