The linear charge density on the upper half of a segment of a ring is $\lambda$ and on the lower half,it is $-\lambda$. The direction of the electric field at the centre $O$ of the ring is:

Find the surface charge density at the intersection of the plane $x = 3 \, m$ and the $x$-axis,given a uniform line charge of $8 \, nC/m$ lying along the $z$-axis in free space.

Obtain the expression for the electric field at any point due to a continuous distribution of charge on a $(i)$ line,$(ii)$ surface,and $(iii)$ volume.

Three identical metal plates with large surface areas are kept parallel to each other as shown in the figure. The leftmost plate $A$ is given a charge $Q$ and the rightmost plate $C$ is given a charge $-2Q$. The middle plate $B$ is neutral. Then the charge appearing on the outer surface $S$ of the plate $C$ is:

$A$ particle of mass $2 \times 10^{-6} \ kg$ with a charge $5 \times 10^{-6} \ C$ is hanging in air above a similarly charged conducting surface. The charge density of the surface is (Assume $\epsilon_0 = 8.85 \times 10^{-12} \ C^2 N^{-1} m^{-2}$ and $g = 10 \ m \ s^{-2}$)

$A$ circle of radius $a$ has a linear charge density given by $\lambda = \lambda_0 \cos^2 \theta$ on its circumference. What will be the total charge on the circle?