Calculation of Electric Potential

What is the potential electric energy of a charged object?

What is the electric potential due to an electric?

What is the electric potential of a point charge?

What is the electric field on the axis of a charged ring?

How much work is done in moving a charge of $2\mathrm{C}$ across two points having a potential difference of $5\mathrm{V}$?

A rod lies along the $\mathrm{x}-$axis with one end at the origin and other at $\mathrm{x}>\infty$ it caries a uniform charge $\mathrm{\lambda } \raisebox{1ex}{$\mathrm{c}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{m}$}\right.$. Find the electric field at the point $\mathrm{x}=-\mathrm{a}$ on the $\mathrm{x}-$axis 

A total charge $\mathrm{Q}$ is distributed uniformly along a straight rod of length $1$. The potential at a point $\mathrm{P}$ at a distance $\mathrm{h}$ from the midpoint of the rod is

Consider a non-conducting rod of length $\mathrm{l}$ having a uniform change density $\mathrm{\lambda }$. Find the electric potential at $\mathrm{P}$ at a perpendicular distance $\mathrm{y}-$above the midpoint of the rod.

The electric potential due to an infinite uniformly charge of linear charge density $\mathrm{\lambda }$ at a distance $\mathrm{r}$ from it is given by ${\mathrm{r}}_{\mathrm{o}}$ is the reference point.

A charge $+q$ is distributed over a thin ring of radius $r$ with line charge density $\lambda =\frac{q{\sin }^2\theta }{\pi r}$. Note that the ring is in the $XY$-plane and $\theta$ is the angle made by $r$ with the $X$-axis. The work done by the electric force in displacing a point charge $+Q$ from the centre of the ring to infinity is

Two identical rings each of radius $R$ are coaxially placed $\mathrm{a}$ distance $R$ apart. They carry charges $Q_1$ and $Q_2$ respectively. If a charge $q$ is moved from the centre of one ring to the centre of the other ring, the work done is

Half of the non-conducting ring has $\left(+Q\right)$ charge and half has $\left(-Q\right)$ charge. Find potential at point $A$ which is on the line passing through centre perpendicular to plane of ring.

A thin ring of radius $R=3 \mathrm{m}$ has been uniformly charged with an amount of $20 \mathrm{\mu }\mathrm{C}$ and placed in relation to a conducting sphere in such a way that the centre of the sphere $\mathrm{O}$, lies on the rings axis at a distance of $l=4 \mathrm{m}$ from the plane of the ring. The potential of the sphere is ………. $\times {10}^4$ volt.

(Given:$\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9 \mathrm{N} {\mathrm{m}}^2 {\mathrm{C}}^{-2}$ )

A thin ring of radius $\mathrm{R}=3\mathrm{m}$ has been uniformly charged with an amount of $20\mathrm{\mu }\mathrm{C}$ and placed in relation to a conducting sphere in such a way that the centre of the sphere $\mathrm{O}$, lies on the rings axis at a distance of $l=4\mathrm{m}$ from the plane of the ring. The potential of the sphere is………. $\times 18\times {10}^3$ volt.

Two thin rings, each of radius $R$, are placed at a distance $d$ apart. The charges on the rings are $+q$ and $-q$, respectively. The potential difference between their centres will be

Two thin rings each of radius $\mathrm{R}$ are placed at a distance $\mathrm{\prime }\mathrm{d}\mathrm{\prime }$ apart. The charges on the rings are $+\mathrm{q}$ and $–\mathrm{q}$. The potential difference between their centres will be -

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

A non-conducting ring of radius $0.5 \mathrm{m}$ carries a total charge of $1.1\times {10}^{-10} \mathrm{C}$ distributed non-uniformly on its circumference producing an electric field $E$, everywhere in space. The value of the line integral, $\underset{l=\infty }{\overset{l=0}{{\displaystyle \int }}}-\overrightarrow{E}.\overrightarrow{dl}$ in S.I. System of units following usual convention, where, $l=0$ is the centre of the ring is:

A non-conducting disc, of radius $a$ and uniform positive surface charge density $\sigma$ is placed on the ground with its axis vertical. A particle of mass $m$ and positive charge $q$ is dropped, along the axis of the disc from a height $H$ with zero initial velocity. The particle has $\frac{q}{m}=\frac{4{\epsilon }_{0}g}{\sigma }$. What is the stable equilibrium position of the particle? 

A non-conducting disc, of radius $a$ and uniform positive surface charge density $\sigma$ is placed on the ground with its axis vertical. A particle of mass $m$ and positive charge $q$ is dropped, along the axis of the disc from a height $H$ with zero initial velocity. The particle has, $\frac{q}{m}=\frac{4{\epsilon }_{0}g}{\sigma }$. What is the value of $H$ if the particle just reaches the disc?