The electric potential at a point in free space due to charge $Q$ coulomb is $V=Q$$ \times {10^{11}}\,V$ . The electric field at that point is
$4\pi {\varepsilon _0}Q \times 10^{20}\;V/m$
$\;12\pi {\varepsilon _0}Q \times {10^{22}}\;V/m$
$\;4\pi {\varepsilon _0}Q \times {10^{22}}\;V/m$
$\;12\pi {\varepsilon _0}Q \times {10^{20}}\;V/m$
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
A spherical charged conductor has surface charge density $\sigma $ . The electric field on its surface is $E$ and electric potential of conductor is $V$ . Now the radius of the sphere is halved keeping the charge to be constant. The new values of electric field and potential would be
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
$A, B$ and $C$ are three points in a uniform electric field. The electric potential is
In a region, the potential is represented by $V(x, y, z) = 6x - 8xy - 8y + 6yz$, where $V$ is in volts and $x, y, z$ are in metres. The electric force experienced by a charge of $2$ coulomb situated at point $( 1, 1, 1)$ is