Assume that an electric field $\overrightarrow E  = 30{x^2}\hat i$ exists in space. Then the potential difference $V_A -V_O$, where $V_O$ is the potential at the origin and $V_A$ the potential at $x = 2\, m$ is

A charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R ( R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is

In an hydrogen atom, the electron revolves around the nucleus in an orbit of radius $0.53 \times {10^{ - 10}}\,m$. Then the electrical potential produced by the nucleus at the position of the electron is......$V$

An infinitely long thin wire, having a uniform charge density per unit length of $5 nC / m$, is passing through a spherical shell of radius $1 m$, as shown in the figure. A $10 nC$ charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points $P$ and $R$, in Volt, is. . . .

[Given: In SI units $\frac{1}{4 \pi \epsilon_0}=9 \times 10^9, \ln 2=0.7$. Ignore the area pierced by the wire.]

The two thin coaxial rings, each of radius $'a'$ and having charges $+{Q}$ and $-{Q}$ respectively are separated by a distance of $'s'.$ The potential difference between the centres of the two rings is :

Two insulated charged conducting spheres of radii $20\,cm$ and $15\,cm$ respectively and having an equal charge of $10\,C$ are connected by a copper wire and then they are separated. Then