Out of two copper spheres of the same size,$x$ is hollow while $y$ is solid. If they are charged at the same potential,what can be said about the charges on them?

$A$ uniformly charged half-ring of radius $R$ has a linear charge density $\sigma$. The electric potential at the centre of the half-ring is ($\epsilon_0$ = permittivity of free space).

$A$ thin spherical shell is charged by some source. The potential difference between the two points $C$ (the center) and $P$ (a point on the surface) as shown in the figure is: (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ SI units}$)

Two concentric hollow conducting spheres of radius $r$ and $R$ $(r < R)$ are shown. The charge on the outer shell is $Q$. What charge $q$ should be given to the inner sphere so that the potential at any point $P$ at a distance $x$ $(x > R)$ from the center is zero?

$A$ and $C$ are concentric conducting spherical shells of radius $a$ and $c$ respectively. $A$ is surrounded by a concentric dielectric of inner radius $a$,outer radius $b$ and dielectric constant $k$. If sphere $A$ is given a charge $Q$,the potential at the outer surface of the dielectric (at radius $b$) is:

$A$ charge $Q$ is uniformly distributed over a long rod $AB$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at a distance $L$ from the end $A$ is