Potential Energy in an External Field

If a system consists of two charges $4 \mathrm{\mu C}$ and $-4 \mathrm{\mu C}$ located at $\left(-3,0,0\right)$ and $\left(3,0,0\right)$ respectively in the presence of external electric field $\frac{9\times {10}^6}{r^2} \mathrm{C} {\mathrm{m}}^{-2}$, then find the electrostatic potential of the given system.

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 

The potential energy of a single charge is measured in Joule which is equal to _____$\times {10}^{18} \mathrm{eV}$ (write the answer up to two decimal places).

A charge of $20\mathrm{\mu C}$ is carried by the potential difference of $10\mathrm{V}$ then potential energy is

$1\mathrm{eV}$ energy is equal to (in joule).

Electrostatic potential energy of single change in absence of external electric field is expressed as $\left(\mathrm{v}=\mathrm{Potential}\right)$

A molecule of a substance has a permanent electric dipole moment equal to ${10}^{-29} \mathrm{C} \mathrm{m}$. A mole of this substance is polarised (at low temperature) by applying a strong electrostatic field of magnitude $\left({10}^6 \mathrm{V} {\mathrm{m}}^{-1}\right)$. The direction of the field is suddenly changed by an angle of $60°$. Estimate the heat released by the substance in aligning its dipoles along the new direction of the field. For simplicity, assume $100\%$ polarisation to the sample.

A dipole is placed in a uniform electric field, its potential energy will be minimum when the angle between its axis and field is zero.

An electric dipole of moment $\overrightarrow{P}$ is placed in a uniform electric field $\overrightarrow{E}$ . Then, the potential energy of the system is $\overrightarrow{P}·\overrightarrow{E}$.

Write the expression for work done in rotating an electric dipole from $0°$ to ${180}^{°}$ in a uniform field.

A body is attached to a spring whose other end is fixed. If the spring is elongated by $x$ . Its potential energy is $U=5x^2,$ where $x$ is in meter and $U$ is in joule. Which of the following depicts the $U-x$ graph ?

A molecule of a substance has a permanent electric dipole moment of magnitude ${10}^{-30} \mathrm{C} \mathrm{m}$. A mole of this substance is polarized by applying a strong electrostatic field of magnitude ${10}^7 \mathrm{V}\mathrm{ }{\mathrm{m}}^{-1}$. The direction of field is changed by an angle $60°$. The heat released by the substance in aligning it's dipole along the new direction of the field is:

A mass of $1\mathrm{k}\mathrm{g}$ carrying a charge of $2 \mathrm{C}$ is accelerated through a potential of $1 \mathrm{V}.$ The velocity acquired by it is

An electric dipole of moment $\overrightarrow{p}$ is lying along a uniform electric field $\overrightarrow{E}.$ The work done in rotating the dipole by ${90}^o$ is

What work must be done to rotate and electric dipole through an angle $\theta$ with the electric field, if an electric dipole of moment p is placed in an uniform electric field E with p parallel to E?

An electric dipole of dipole moment $\overrightarrow{P}$is placed in a uniform electric field $\overrightarrow{\mathit{E}}$ such that, $\overrightarrow{P}$ is perpendicular to $\overrightarrow{E}$. The work done to turn the dipole through an angle of $180°$ is

In which of the states, shown in the figure is the potential energy of a electric dipole maximum?

A 100 eV electron is fired directly towards a large metal plate having surface charge density $-2\times {10}^{-6 }\mathrm{c}{\mathrm{m}}^{-2}.$ The distance from where the electrons be projected so that it just fails to strike the plate is

An electric dipole of moment p placed in a uniform electric field E has minimum potential energy when the angle between p and E is

An electric dipole has the magnitude of its charge as $q$ and its dipole moment is $p$. It is placed in uniform electric field $E$. If its dipole moment is along the direction of the field, the force on it and its potential energy are