If potential (in volts) in a region is expressed as $V (x,y,z) =6xy-y+2yz $ the electric field (in $N/C$) at point $(1, 1, 0)$ 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.

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 sphere carrying charge of $Q$ having weight $w$ falls under gravity between a pair of vertical plates at a distance of $d$ from each other. When a potential difference $V$ is applied between the plates the acceleration of sphere changes as shown in the figure, to along line $BC$. The value of $Q$ is :-

The figure gives the electric potential $V$ as a function of distance through five regions on $x$-axis. Which of the following is true for the electric field $E$ in these regions

Electric potential at any point is $V = - 5x + 3y + \sqrt {15} z$, then the magnitude of the electric field is