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

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

Electric potential is given by

$V = 6x - 8x{y^2} - 8y + 6yz - 4{z^2}$

Then electric force acting on $2\,C$ point charge placed on origin will be......$N$

Consider a gravity free container as shown. System is initially at rest and electric potential in the regon is $V = (y^3+2)\  J/C$. A ball of charge $q$ and mass $m$ is released from rest from base starts to move up due to electric field and collides with the shaded face as shown.If its speed just after collision is $1.5\  m/s$ and time for which ball is in contact with shaded face is $0.1\ sec$, find external force required to hold the container fixed in its position during collision assuming ball exerts constant force on wall during entire span of collision.......$N$

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 variation of potential with distance $x$ from a fixed point is as shown in figure. The electric field at $x =13\,m$ is......$volt/meter$