Charges $Q, 2Q$ and $-Q$ are given to three concentric conducting shells $A, B$ and $C$ respectively as shown. The ratio of charges on the inner and outer surfaces of shell $C$ will be:

$A$ 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 $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \text{ N} \cdot \text{m}^2 / \text{C}^2$)

The surface charge density $\sigma$ on a charged conducting sphere of radius $R$ in terms of the electric field intensity $E$ at a distance $r$ $(r > R)$ in free space is (where $\varepsilon_{0}$ is the permittivity of free space):

$A$ square plate of side $a$ is placed in the $xy$-plane with its center at the origin. If the surface charge density of the square plate is given by $\sigma = xy$,then the total charge on the plate will be:

$A$ 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?

$A$ 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: