If the electric potential at any point $(x, y, z) \,m$ in space is given by $V =3 x ^{2}$ volt. The electric field at the point $(1,0,3) \,m$ will be ............
$3 \,Vm ^{-1}$, directed along positive $x$-axis
$3 \,Vm ^{-1}$, directed along negative $x$-axis
$6 \,Vm ^{-1}$, directed along positive $x$-axis
$6 \,Vm ^{-1}$, directed along negative $x$-axis
The electrostatic potential inside a charged spherical ball is given by : $V = b -ar^2$, where $r$ is the distance from the centre ; $a$ and $b$ are constants. Then, the charge density inside the ball is :
The diagram below shows electric field lines in a region of space. Which of the following diagrams best shows the variation with distance $d$ of the potential $V$ along the line $XY$ as we move from $X$ to $Y$ ?
If on the $x$-axis electric potential decreases uniformly from $60 \,V$ to $20 \,V$ between $x=-2 \,m$ to $x=+2 \,m$, then the magnitude of electric field at the origin
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.....$s$
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