The given diagram shows two semi-infinite lines of charge having equal (in magnitude) linear charge density but with opposite signs. The electric field at any point on the $x$-axis for $(x > 0)$ is along the unit vector:

Three isolated metal spheres $A$,$B$,and $C$ have radii $R$,$2R$,and $3R$ respectively,and the same charge $Q$. If $U_A$,$U_B$,and $U_C$ are the energy densities just outside the surfaces of the spheres,then the relation between $U_A$,$U_B$,and $U_C$ is:

What is the magnitude of a point charge due to which the electric field $30\,cm$ away has the magnitude $2\,N/C$ $[1/4\pi \varepsilon_0 = 9 \times 10^9\,N\cdot m^2/C^2]$?

An infinite number of electric charges,each with a magnitude of $5 \, nC$,are placed along the $X$-axis at $x = 1 \, cm$,$x = 2 \, cm$,$x = 4 \, cm$,$x = 8 \, cm$,and so on. If the consecutive charges have opposite signs,find the electric field in $N/C$ at $x = 0$. (Given: $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9 \, N \cdot m^2/C^2$)

Five point charges each having magnitude $q$ are placed at the corners of a regular hexagon as shown in the figure. The net electric field at the centre $O$ is $\vec E$. To make the net electric field at $O$ equal to $6\vec E$,the charge placed on the remaining sixth corner should be: (in $,q$)

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 $g = 10 \ m \ s^{-2}$ and charge on an electron $e = 1.6 \times 10^{-19} \ C$):