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

The potential $V$ is varying with $x$ and $y$ as $V\, = \,\frac{1}{2}\,\left( {{y^2} – 4x} \right)\,volt.$ The field at ($1\,m, 1\,m$ ) is

A cathode ray tube contains a pair of parallel metal plates $1.0\, cm$ apart and $3.0\, cm$ long. A narrow horizontal beam of electron with a velocity $3 \times 10^7\, m/s$ passed down the tube midway between the plates. When a potential difference of $550\, V$ is maintained across the plates, it is found that the electron beam is so deflected that it just strikes the end of one of the plates. Then the specific charge of the electron in $C/kg$ is

Which of the following is true for the figure showing electric lines of force? ($E$ is electrical field, $V$ is potential)