Potential Due to a Point Charge

Electric potential due to point charge in air is expressed as $\mathrm{V}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}·\frac{\mathrm{q}}{\mathrm{r}}$ as $\mathrm{V}\propto \frac{1}{\mathrm{r}}$. i.e for $\mathrm{r}=0$ to $\mathrm{r}=\infty$ potential varies 

The graph of variation of potential due to point charge vs distance is said to be symmetric

Electric potential due to point charge in air is expressed as $\mathrm{V}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}·\frac{\mathrm{q}}{\mathrm{r}}$ as $\mathrm{V}\propto \frac{1}{\mathrm{r}}$. i.e for $\mathrm{r}=0$ to $\mathrm{r}=\infty$ potential varies 

Which of the follow graph is correct for potential due to point charge at any point versus distance as shown in figure.

The graph of variation of potential due to point charge vs distance is said to be _____ symmetric

A metallic sphere A isolated from the ground is charged to $+50 \mu \mathrm{C}$. This sphere is brought in contact with other isolated metallics sphere B of half the radius of sphere A. The charge on the two sphere will now be in the ratio

What is the electric potential at a point $1 \mathrm{m}$ distance from a point charge of ${10}^{-9}$ coulomb? Round it to the nearest integer.

The potential at a point $P$ due to a charge of $4\times {10}^{-7} \mathrm{C}$ located $9 \mathrm{cm}$ away is (Assume $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9 \mathrm{N} {\mathrm{C}}^{-2} {\mathrm{m}}^2$)

An electric charge ${10}^{–3}\mathrm{\mu }\mathrm{C}\mathrm{ }$ is placed at the origin$\mathrm{ }\left(0,\mathrm{ }0\right)$. Two points $\mathrm{A}$ and $\mathrm{B}$ are situated at $\left(\sqrt{2}\mathrm{¸}\sqrt{2}\right)$ and $\left(2,\mathrm{ }0\right)$ respectively. The potential difference between the points $\mathrm{A}$ and $\mathrm{B}$ will be

The electric potential due to a point charge at some point in free space is $10 \mathrm{V}$. If the entire system is now placed in a dielectric medium of dielectric constant $2$. What will be the potential at the same point in volt?

Show that the electric potential due to a point charge when surrounded by some dielectric medium is $1/{\epsilon }_{\mathit{r}}$ times of the electric potential when the charge is in free space.

A charge of $10 \mathrm{\mu C}$ is located at the origin of $\mathrm{X}-\mathrm{Y}$ coordinate system. The potential difference between points $(\mathrm{a}, 0)$ and $\left(\frac{\mathrm{a}}{\sqrt{2}},\frac{\mathrm{a}}{\sqrt{2}}\right)$ is

The electric potential is $+100 \mathrm{V}$ at a distance of $10 \mathrm{c}\mathrm{m}$ from a point charge $q.$ Then, $q$ is equal to

If three point charges are placed at the three corners of a square of diagonals $2a$ as shown in the figure. Then, ${\int }_B^A\overrightarrow{E}.\overrightarrow{dr}$ will be

There are four sphere of each  with radius as $\mathrm{a}$,$\mathrm{ }\mathrm{b}$, $\mathrm{c}$, $\mathrm{d}$, each sphere is solid, insulating and uniformly charged. Variation of electric field with distance $\mathrm{r}$ from the centre is given. Straight portion of curve $\mathrm{c}$ and $\mathrm{d}$ is overlapping and straight portion of curve $\mathrm{a}$ and $\mathrm{b}$ is overlapping.

Four charges of $6\mathrm{\mu }\mathrm{C}$, $2\mathrm{\mu }\mathrm{C}$, $–\mathrm{ }12\mathrm{\mu }\mathrm{C}$ and $4\mathrm{\mu }\mathrm{C}$ are placed at the corners of a square of side $1\mathrm{m}$. The square is in $\mathrm{x}-\mathrm{y}$ plane and its center at its origin. Electric potential due to these charges is zero everywhere on the line -

Two equal point charges are fixed at $x=–a$ and $x=+a$, on the $x$-axis. Another point charge $Q$ is placed at the origin. The change in the electrical potential energy of $Q$, when it is displaced by a small distance $x$, along $x$-axis, is approximately proportional to

A square of side $a$ has charge $Q$ at its centre and charge $q$ at one of the corners. The work required to be done in moving the charge $q$ from the corner to the diagonally opposite corner is

An electric charge ${10}^{-3} \mathrm{C}$ is placed at the origin $\left(0, 0\right)$ of $X-Y$ coordinate system. Two points $A$ and $B$ are situated at $\left(\sqrt{2}, \sqrt{2}\right)$ and $\left(2, 0\right)$ respectively. The potential difference between the points $A$ and $B$ will be,

Two charges, $+q$ and $-q$, are kept apart. Then, at any point on the right bisector of line joining the two charges,