The electric potential $V$ at any point $(x, y, z)$ in space is given by the equation $V = 4x^2 \, V$,where $x, y$,and $z$ are all in meters. The electric field at the point $(1 \, m, 0, 2 \, m)$ in $V/m$ is:

If the electric potential at any point $(x, y, z) \, m$ in space is given by $V = 3x^2$ volt,the electric field at the point $(1, 0, 3) \, m$ will be ............

For a charged spherical ball,electrostatic potential inside the ball varies with $r$ as $V = 2ar^2 + b$. Here,$a$ and $b$ are constants and $r$ is the distance from the center. The volume charge density inside the ball is $-\lambda a \varepsilon$. The value of $\lambda$ is $...........$. $\varepsilon =$ permittivity of medium.

Electric potential is given by $V = 6x - 8xy^2 - 8y + 6yz - 4z^2$. Then,the electric force acting on a $2 \, C$ point charge placed at the origin will be......$N$.

In a region,the electric field is $(30 \hat{i} + 40 \hat{j}) \text{ NC}^{-1}$. If the electric potential at the origin is zero,the electric potential at the point $(1 \text{ m}, 2 \text{ m})$ is

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