Determine the electric field strength vector if the potential of this field depends on $x, y$ coordinates as $V=10$ axy
$10 a(y \hat{i}+x \hat{j})$
$-10 a[y \hat{i}+x \hat{j}]$
$-a[y \hat{i}+x \hat{j}]$
$-10 a[x \hat{i}+y \hat{k}]$
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
Figure shows two equipotential lines in $x, y$ plane for an electric field. The scales are marked. The $x-$ component $E_x$ and $y$ -component $E_y$ of the electric field in the space between these equipotential lines are respectively :-
An oil drop having charge $2e$ is kept stationary between two parallel horizontal plates $2.0\, cm$ apart when a potential difference of $12000\, volts$ is applied between them. If the density of oil is $900 \,kg/m^3$, the radius of the drop will be
The electric potential at a point $(x,\;y)$ in the $x - y$ plane is given by $V = - kxy$. The field intensity at a distance $r$ from the origin varies as
The electric potential $V$ at any point $O$ ($x$, $y$, $z$ all in metres) in space is given by $V = 4{x^2}\,volt$. The electric field at the point $(1m,\,0,\,2m)$ in $volt/metre$ is