A non-conducting ring of radius $0.5\,m$ carries a total charge of $1.11 \times {10^{ – 10}}\,C$ distributed non-uniformly on its circumference producing an electric field $\vec E$ everywhere in space. The value of the line integral $\int_{l = \infty }^{l = 0} {\, – \overrightarrow E .\overrightarrow {dl} } \,(l = 0$ being centre of the ring) in volt is

There is a uniformly charged non conducting solid sphere made of material of dielectric constant one. If electric potential at infinity be zero, then the potential at its surface is $V$. If we take electric potential at its surface to be zero, then the potential at the centre will be

Point charge ${q_1} = 2\,\mu C$ and ${q_2} = – 1\,\mu C$ are kept at points $x = 0$ and $x = 6$ respectively. Electrical potential will be zero at points

Consider a sphere of radius $R$ with uniform charge density and total charge $Q$. The electrostatic potential distribution inside the sphere is given by $\theta_{(r)}=\frac{Q}{4 \pi \varepsilon_{0} R}\left(a+b(r / R)^{C}\right)$. Note that the zero of potential is at infinity. The values of $(a, b, c)$ are

The electric field $\vec E$ between two points is constant in both magnitude and direction. Consider a path of length d at an angle $\theta = 60^o$ with respect to field lines shown in figure. The potential difference between points $1$ and $2$ is