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)

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

The electric potential at any point as a function of distance $(x)$ in meter is given by  $V = 5x^2 + 10x -9 \,(volt)$ Value of electric field at $x = 1$ is……$Vm^{-1}$

An electron enters between two horizontal plates separated by $2\,mm$ and having a potential difference of $1000\,V$. The force on electron 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