The electric potential at a point $(x,\;y)$ in the $x - y$ plane is given by $V = - kxy$. The field intensity at a distance $r$ from the origin varies as

A charge $3$ coulomb experiences a force $3000$ $N$ when placed in a uniform electric field. The potential difference between two points separated by a distance of $1$ $cm$ along the field lines is.....$V$

In a certain region of space, variation of potential with distance from origin as we move along $x$-axis is given by $V=8 x^2+2$, where $x$ is the $x$-coordinate of a point in space. The magnitude of electric field at a point $(-4,0)$ is .......... $V / m$

A charge of $5\,C$ experiences a force of $5000\,N$ when it is kept in a uniform electric field. .........$V$ is the potential difference between two points separated by a distance of $1\,cm$

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