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:

$A$ parallel plate capacitor has a potential of $20 \ kV$ and a capacitance of $2 \times 10^{-4} \ \mu F$. If the area of the plate is $0.01 \ m^2$ and the distance between the plates is $2 \ mm$,find the potential gradient.

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.

The variation of potential $V$ with distance $x$ from a fixed point is as shown in the figure. The electric field at $x = 13\,m$ is......$V/m$.

The electric potential in a region is represented as $V = 2x + 3y - z$. The expression for the electric field strength is:

The electric potentials of two plates are $-10\, V$ and $+30\, V$ respectively. If the distance between the two plates is $2\, cm$,then the electric field between them is ... $V/m$.