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

The electric potential in some region is expressed by $V = 6x - 8xy^2 - 8y + 6yz - 4z^2 \text{ volt}$. The magnitude of the electric force acting on a charge of $2 \text{ C}$ situated at the origin will be $-$ (in $\text{ N}$)

In which region is the magnitude of the $x$-component of the electric field maximum,if the potential $(V)$ versus distance $(X)$ graph is as shown?

If the electric potential is given by $V = (5x^2 + 10x - 9) \ V$,what is the electric field at $x = 1 \ m$ in $V/m$?

An infinite non-conducting sheet has a surface charge density of $7 \times 10^{-7} \text{ C m}^{-2}$ on one side. The distance between equipotential surfaces whose potentials differ by $19.8 \text{ V}$ will be (Take $\frac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^9 \text{ SI units}$) (in $\text{ mm}$)

$A$ small particle carrying a negative charge of $1.6 \times 10^{-19} \text{ C}$ is suspended in equilibrium between two horizontal metal plates $8 \text{ cm}$ apart having a potential difference of $980 \text{ V}$ across them. Find the mass of the particle. $[g = 9.8 \text{ m/s}^2]$