The maximum electric field that can be held in air without producing ionisation of air is $10^7\,V/m$. The maximum potential therefore, to which a conducting sphere of radius $0.10\,m$ can be charged in air 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 $V(x)$ in a region around the origin is given by $V(x) = 4x^2\,volts$ . The electric charge enclosed in a cube of $1\,m$ side with its centre at the origin is (in coulomb)

$A, B$ and $C$ are three points in a uniform electric field. The electric potential is

For a charged spherical ball, electrostatic potential inside the ball varies with $r$ as $V =2 ar ^2+ b$. Here, $a$ and $b$ are constant 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 at any point is $V = - 5x + 3y + \sqrt {15} z$, then the magnitude of the electric field is