In the absence of other conductors,the surface charge density is:

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:

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.

$A$ point charge $q = 1 \mu C$ is located at a distance $2 \text{ cm}$ from one end of a thin insulating wire of length $L = 10 \text{ cm}$ having a charge $Q = 24 \mu C$, distributed uniformly along its length, as shown in the figure. The force between $q$ and the wire is . . . . . . $N$. (Use $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \text{ N} \cdot \text{m}^2 / \text{C}^2$)

Each of two large conducting parallel plates has one-sided surface area $A$. If one of the plates is given a charge $Q$ whereas the other is neutral,then the electric field at a point in between the plates is given by

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: