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.

Two parallel plates separated by a distance of $5\,mm$ are kept at a potential difference of $50\,V.$ A particle of mass ${10^{ - 15}}\,kg$ and charge ${10^{ - 11}}\,C$ enters in it with a velocity ${10^7}\,m/s.$ The acceleration of the particle will be

Variation of electrostatic potential along $x$-direction is shown in the graph. The correct statement about electric field is

Electric potential is given by

$V = 6x - 8x{y^2} - 8y + 6yz - 4{z^2}$

Then electric force acting on $2\,C$ point charge placed on origin will be......$N$

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)

The electric potential varies in space according to the relation $V = 3x + 4y$. A particle of mass $0.1\,\, kg$ starts from rest from point $(2, 3·2)$ under the influence of this field. The charge on the particle is $+1\,\, μC$. Assume $V$ and $(x, y)$ are in $S.I.$ $units$ . The time taken to cross the $x-$ axis is.....$s$