Determine the electric field strength vector if the potential of this field depends on $x, y$ coordinates as $V = 10axy$.

The electric potential $V(x, y, z)$ for a planar charge distribution is given by:
$V(x, y, z) = \begin{cases} 0 & \text{for } x < -d \\ -V_0(1 + \frac{x}{d})^2 & \text{for } -d \le x < 0 \\ -V_0(1 + 2\frac{x}{d}) & \text{for } 0 \le x < d \\ -3V_0 & \text{for } x \ge d \end{cases}$
where $-V_0$ is the potential at the origin and $d$ is a distance. The graph of the electric field as a function of position is:

The potential function of an electrostatic field is given by $V = 2x^2$. Determine the electric field strength at the point $(2 \ m, 0, 3 \ m)$.

The electric potential $V$ is given as a function of distance $x$ (metre) by $V = (5x^2 + 10x - 9) \text{ V}$. The value of the electric field at $x = 1 \text{ m}$ is ...... $V/m$.

Write the relation between electric field and electrostatic potential.

Let $V$ and $E$ be the potential and electric field intensity at a point,respectively. Then: