The potential at a point $x$ (measured in $μ\ m$) due to some charges situated on the $ x$-axis is given by $V(x)$ =$\frac{{20}}{{{x^2} – 4}}$ $volt$ The electric field $E$ at $x = 4\ μ m$ is given by

The electric potential at a point $(x, y, z)$ is given by $V=-x^2y-xz^3 +4 $. The electric field at that point is  

Two large circular discs separated by a distance of $0.01 m$ are connected to a battery via a switch as shown in the figure. Charged oil drops of density $900 kg m ^{-3}$ are released through a tiny hole at the center of the top disc. Once some oil drops achieve terminal velocity, the switch is closed to apply a voltage of $200 V$ across the discs. As a result, an oil drop of radius $8 \times 10^{-7} m$ stops moving vertically and floats between the discs. The number of electrons present in this oil drop is (neglect the buoyancy force, take acceleration due to gravity $=10 ms ^{-2}$ and charge on an electron ($e$) $=1.6 \times 10^{-19} C$ )

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 potential function of an electrostatic field is given by $V = 2x^2$. Determine the electric field strength at the point $(2\,m, 0, 3\,m)$