An infinite line charge produces a field of $9 \times 10^4 \text{ NC}^{-1}$ at a distance of $2 \text{ cm}$. Calculate the electric field produced at a distance of $3 \text{ cm}$.

$A$ thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel at $5 \ m$ distance from each other. Points $P$ and $Q$ are at $\frac{3}{\pi} \ m$ and $\frac{4}{\pi} \ m$ perpendicular distance from the line charge towards the sheet charge,respectively. $E_P$ and $E_Q$ are the magnitudes of the resultant electric field intensities at points $P$ and $Q$,respectively. If $\frac{E_P}{E_Q} = \frac{4}{a}$ for $2|\sigma| = |\lambda|$,then the value of $a$ is ...........

$A$ charge of $1 \mu C$ each is placed on five corners of a regular hexagon of side $1 \ m$. The electric field at its centre is . . . . . . $N$/$C$.

Three charged particles $A, B$ and $C$ with charges $-4q, 2q$ and $-2q$ are present on the circumference of a circle of radius $d$. The charged particles $A, C$ and the centre $O$ of the circle form an equilateral triangle as shown in the figure. The electric field at $O$ along the $x$-direction is

Point charges $+8q$ and $-2q$ are placed at $x = 0$ and $x = L$ respectively. At which point on the $X$-axis will the resultant electric field intensity be zero?

The insulation property of air breaks down at $E = 3 \times 10^6 \ V/m$. The maximum charge that can be given to a sphere of diameter $5 \ m$ is approximately (in coulombs):