Two infinitely long parallel wires have linear charge densities $\lambda_1$ and $\lambda_2$ respectively. They are placed at a distance $R$ apart. The force per unit length on the wires will be ......

$A$ metallic ring is uniformly charged as shown in the figure. $AC$ and $BD$ are two mutually perpendicular diameters. The magnitude of the electric field at $O$ due to arc $AB$ is $E$. What would be the magnitude of the electric field at $O$ due to arc $ABC$?

$A$ 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 ...........

$A$ wire of length $L = 20 \, cm$ is bent into a semicircular arc. If the two equal halves of the arc are uniformly charged with charges $+Q$ and $-Q$ respectively,where $|Q| = 10^3 \varepsilon_0$ Coulomb and $\varepsilon_0$ is the permittivity of free space,find the net electric field at the centre $O$ of the semicircular arc.

Two non-conducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\rho$ and $-\rho$,respectively,are placed such that they partially overlap,as shown in the figure. At all points in the overlapping region:
$(A)$ the electrostatic field is zero
$(B)$ the electrostatic potential is constant
$(C)$ the electrostatic field is constant in magnitude
$(D)$ the electrostatic field has same direction

Two charged particles, each with a charge of $+q$, are located along the $x$-axis at $x = 2$ and $x = 4$, as shown below. Which of the following shows the graph of the magnitude of the electric field along the $x$-axis from the origin to $x = 6$?