Electric Potential and Potential Energy

A particle of charge+q and mass m moving under the influence of a uniform electric field E $\widehat{\text{i}}\text{and magnetic field B}\widehat{\text{k}}$enters in I quadrant of a coordinate system at a point (0, a) with initial velocity v$\widehat{\text{i}}$and leaves the quadrant at a point (2a, 0) with velocity $-\mathrm{2 }\text{v}\widehat{\text{j}}$.
Find Rate of work done by the electric field at point (0, a)

The term ‘potential energy’ of charge ‘q’ at a distance ‘r’ in an external electric field can be defined as:.

A charge $+Q$ is placed on a large spherical conducting shell of radius $R$. Another small conducting sphere of radius r carrying charge $q$ is introduced inside the large shell and is placed at its centre. The potential difference between two points, one lying on the sphere and the other on the shell would be:

Two point’s charges $q_1, q_2$ , initially at infinity, are brought one by one to points $P_1$ and $P_2$ , specified by position vectors $\overrightarrow{r_1}$ and $\overrightarrow{r_2}$ , relative to some origin. What is the potential energy of this charge configuration?

How does the electric potential due to a dipole vary on the dipole axis as a function of $r$– distance of the field point from the mid–point of the dipole, at large distances?

Two point charges  $20\times {10}^{-6}$ C and  $-4\times {10}^{-6}$ C are separated by a distance of 50 cm in air.

(i) Find the point on the line joining the charges, where the electric potential is zero.

(ii) Also find the electrostatic potential energy of the system.

Three charges, $-q,\mathrm{ }Q$ and $-q$, are placed at equal distances, on a straight line. If the potential energy of the system of three charges is zero, then what is the ratio of $Q:q$?

Three charges, $-q,\mathrm{ }Q$ and $-q$, are placed at equal distances, on a straight line. If the potential energy of the system of three charges is zero, then what is the ratio of $Q:q$?

Which of the following statements are correct? If the potential along the straight line joining the two charges $Q_1$ and $Q_2$, separated by a distance $r$, is represented as shown in the figure below.

1. $\left|{\mathrm{Q}}_1\right|>\left|{\mathrm{Q}}_2\right|$
2. $Q_1$ is positive in nature
3. $A \mathrm{and} B$ are equilibrium points
4. $C$ is a point of unstable equilibrium along $X$ axis.

If the potential difference between the surface of hollow charged metal sphere of radius $r$ and a point at a distance $3r$ from the centre is $V$, then the electric intensity at a distance $3r$ from the centre is-

Two positive charges $12 \mathrm{\mu C}$ and $8 \mathrm{\mu C}$ are $10 \mathrm{cm}$ apart. The work done in bringing them closer to $4 \mathrm{cm}$ is

An uncharged conductor $A$ is brought near a positively charged conductor $B$, then :

When a charge $2 \mathrm{\mu C}$ is carried from point $A$ to point $B$, the amount of work done by the electric field is $50 \mathrm{\mu J}$. What is the potential difference and which is at a higher potential?

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

The electrostatic energy of a nucleus of charge $Ze$ is equal to $k{Z}^2{e}^2/R$, where $k$ is a constant and $R$ is the nuclear radius. The nucleus divides into two daughter nuclei of charges $Ze/2$ and equal radii. The change in electrostatic energy in the process when they are far apart is

Two point charges ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ are repatriated by distance $\text{'}\mathrm{r}\text{'}$ in in external electric field. Potential energy $\mathrm{U}$ is expressed as $\mathrm{U}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}·\mathrm{x}$

value of $\mathrm{x}$ is 

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.