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 ......

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 $e = 1.6 \times 10^{-19} \ C$):

$A$ spherical conductor of radius $10 \, cm$ has a charge of $3.2 \times 10^{-7} \, C$ distributed uniformly. What is the magnitude of the electric field at a point $15 \, cm$ from the centre of the sphere?
$\left(\frac{1}{4 \pi \epsilon_{0}} = 9 \times 10^{9} \, Nm^{2}/C^{2}\right)$

The variation of electric field along the $Z$-axis due to a uniformly charged circular ring of radius '$a$' in the $XY$ plane is shown in the figure. The value of coordinate $M$ will be

The three charges $q/2, q$ and $q/2$ are placed at the corners $A, B$ and $C$ of a square of side '$a$' as shown in the figure. The magnitude of the electric field $(E)$ at the corner $D$ of the square is:

If the net electric field at point $P$ along the $Y$-axis is zero,then the ratio of $\left|\frac{q_2}{q_3}\right|$ is $\frac{8}{5 \sqrt{x}}$,where $x = . . . . . .$