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:

$A$ disc of radius $R$ is charged on its surface with surface charge density $\sigma = \sigma_0 r^3$. Here $\sigma_0$ is a constant and $r$ is the distance from its centre. The total charge on the disc is:

Three identical metal plates with large surface areas are kept parallel to each other as shown in the figure. The leftmost plate is given a charge $Q$,the rightmost a charge $-2Q$,and the middle one remains neutral. Find the charge appearing on the outer surface of the rightmost plate.

The electric flux is $\phi = \alpha \sigma + \beta \lambda$,where $\lambda$ and $\sigma$ are linear and surface charge density,respectively. The ratio $\left(\frac{\alpha}{\beta}\right)$ represents:

Charge is distributed within a sphere of radius $R$ with a volume charge density $\rho (r) = \frac{A}{r^2} e^{-2r/a}$,where $A$ and $a$ are constants. If $Q$ is the total charge of this charge distribution,the radius $R$ is:

$A$ point charge $q$ is situated at a distance $r$ on the axis from one end of a thin conducting rod of length $L$ having a charge $Q$ (uniformly distributed along its length). The magnitude of the electric force between the two is . . . . . . .