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 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…..$s$

A uniform electric field having a magnitude ${E_0}$ and direction along the positive $X – $ axis exists. If the potential $V$ is zero at $x = 0$, then its value at $X = + x$ will be

In a certain region of space, the potential is given by : $V = k[2x^2 – y^2 + z^2].$ The electric field at the point $(1, 1, 1) $ has magnitude =

The potential gradient is a