The potential function of an electrostatic field is given by $V = 2x^2$. Determine the electric field strength at the point $(2\,m, 0, 3\,m)$

Within a spherical charge distribution of charge density $\rho \left( r \right)$, $N$ equipotential surfaces of potential ${V_0},{V_0} + \Delta V,{V_0} + 2\Delta V,$$.....{V_0} + N\Delta V\left( {\Delta V > 0} \right),$ are drawn and have increasing radii $r_0, r_1, r_2,......r_N$, respectively. If the difference in the radii of the surfaces is constant for all values of $V_0$ and $\Delta V$ then

The electric potential varies in space according to the relation $V = 3x + 4y$. A particle of mass $0.1\,\, kg$ starts from rest from point $(2, 3·2)$ under the influence of this field. The charge on the particle is $+1\,\, μC$. Assume $V$ and $(x, y)$ are in $S.I.$ $units$ . The time taken to cross the $x-$ axis is.....$s$

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 :

Two large circular discs separated by a distance of $0.01 m$ are connected to a battery via a switch as shown in the figure. Charged oil drops of density $900 kg m ^{-3}$ are released through a tiny hole at the center of the top disc. Once some oil drops achieve terminal velocity, the switch is closed to apply a voltage of $200 V$ across the discs. As a result, an oil drop of radius $8 \times 10^{-7} m$ stops moving vertically and floats between the discs. The number of electrons present in this oil drop is (neglect the buoyancy force, take acceleration due to gravity $=10 ms ^{-2}$ and charge on an electron ($e$) $=1.6 \times 10^{-19} C$ )

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