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.

If a solid and a hollow conducting sphere have the same radius, then:

Three concentric metallic spherical shells of radii $R, 2R, 3R$ are given charges $Q_1, Q_2, Q_3$ respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then,the ratio of the charges given to the shells,$Q_1 : Q_2 : Q_3$,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 . . . . . . .

$A$ 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:

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