Potential Due to a Point Charge

Two charges each of$+40 \mathrm{\mu C}$  are placed at distance of $0.4 \mathrm{m}$ calculate the potential at the midpoint if dielectric constant of the medium is $2$.

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

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

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.

Let $V$ be the electric potential at a given point. Then the electric field $E_x$ along $x$-direction at that point is given by,

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

The electric potential at a point in free space due to a charge $Q$ coulomb is $Q\times {\mathrm{10}}^{11} \mathrm{V}$. The electric field at that point is

Charges $+q$ and $-q$ are placed at points $A$ and $B$, respectively which are a distance $2L$ apart, $C$ is the midpoint between $A$ and $B$. The work done in moving a charge $+Q$ along the semicircle $CRD$ is: