The point charges $Q$ and $-2Q$ are placed at a distance $r$ apart. If the electric field at the location of $Q$ (point $A$) due to $-2Q$ is $\vec E$,then the electric field at the location of $-2Q$ (point $B$) due to $Q$ will be:

The point charges $+q, -q, -q, +q, +Q$ and $-q$ are placed at the vertices $A, B, C, D, E$ and $F$ respectively of a regular hexagon $ABCDEF$. The electric field at the centre of the hexagon '$O$' due to the five charges at $A, B, C, D$ and $F$ is thrice the electric field at centre '$O$' due to charge $+Q$ at $E$ alone. The value of $Q$ is

The energy density of an electric field is proportional to which of the following?

$A$ thin metallic wire having a cross-sectional area of $10^{-4} \, m^2$ is used to make a ring of radius $30 \, cm$. $A$ positive charge of $2 \pi \, pC$ is uniformly distributed over the ring, while another positive charge of $30 \, pC$ is kept at the centre of the ring. The tension in the ring is . . . . . . $N$; provided that the ring does not get deformed (neglect the influence of gravity). (Given, $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \, SI$ units)

For a uniformly charged ring of radius $R$,the electric field on its axis has the largest magnitude at a distance $h$ from its centre. Then the value of $h$ is

Two identical point charges are placed at a separation of $d$. $P$ is a point on the line joining the charges, at a distance $x$ from any one charge. The field at $P$ is $E$. $E$ is plotted against $x$ for values of $x$ from close to zero to slightly less than $d$. Which of the following represents the resulting curve?