The electric potential as a function of $x, y$ is given by $V = 5(x^2 - y^2) \text{ V}$. The electric field at a point $(2, 3) \text{ m}$ is . . . . . . $\text{V/m}$.

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?

The electric potential at a point $(x, y, z)$ is given by $V = -x^2y - xz^3 + 4$. The electric field at that point is:

Two points $A$ and $B$ on the $Y$-axis are at distances of $12.3 \ cm$ and $12.5 \ cm$ from the origin,respectively. The potentials at these points are $56 \ V$ and $54.8 \ V$,respectively. What is the component of the force on a charge of $4 \ \mu C$ placed at point $A$ on the $Y$-axis?

$A$ 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. $[g = 9.8 \text{ m/s}^2]$

The figure shows the electric potential $V$ as a function of distance through five regions on the $x$-axis. Which of the following is true for the electric field $E$ in these regions?