Potential Energy in an External Field

Two point charges 4Q,Q are separated by 1 m in air at what point on the line joining the charges is the electric field intensity zero?

Also calculate the electrostatic potential energy of the system of charges, taking the value of charge,  $Q=2\times {10}^{-7}$ C.

An electric dipole of dipole moment is $6.0 \times {10}^{-6} \mathrm{C} \mathrm{m}$ placed in a uniform electric field of $1.5 \times {10}^3 \mathrm{N} {\mathrm{C}}^{-1}$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $180°$in this field will be_______$\mathrm{mJ}$.

A free point charge $q$ of mass $m$ is at rest at the origin as shown in the figure. A constant electric field $E_0\hat{\mathrm{i}}+E_0\hat{\mathrm{j}}$ and a constant magnetic field $B\left(-\hat{\mathrm{k}}\right)$ is present in whole region. When this charge reaches at position $(2, 2, 0)$, its speed will be $\sqrt{\frac{kq{E}_0}{m}}$. Find $k$

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A large metal plate has a surface charge density of $8.85\times {10}^{-6} \mathrm{C} {\mathrm{m}}^{-2}$. An electron having initial kinetic energy of $8\times {10}^{-17} \mathrm{J}$ is moving towards the center of the plate. If the electron stops just before reaching the plate then the initial distance between the electron and the plate is [Take ${\epsilon }_0=8.85\times {10}^{-12} {\mathrm{C}}^2 \mathrm{N} {\mathrm{m}}^{-2}$]

If an electric dipole of moment $\left(P\right)$ is placed in a uniform electric field $\left(E\right)$ and making an angle $\left(\theta \right)$ with electric field, the potential energy of the electric dipole is

A dipole is placed in a uniform electric field such that potential energy of a dipole is minimum $\left(U\right)$. The work done by the external agent in rotating dipole by $180°$ is

If potential energy of a dipole is chosen to be zero when dipole moment vector makes angle $\frac{\pi }{3}$ with uniform electric field $E$. Then potential energy when dipole moment vector becomes parallel to electric field will become

Electrostatic Energy density is always positive but energy between a postive and negative charge is negative

One half of a semicircular ring of radius $R$ has charge $-Q$ while the other half has $+Q$. The ring is placed in $xy$ plane where a uniform electric field exists $\overrightarrow{E}=E_0\hat{\mathrm{i}}$

Find the work required to be done by external agent to rotate the ring about $z$ axis by $90°$ in clockwise direction.

One half of a semicircular ring of radius $R$ has charge $-Q$ while the other half has $+Q$. The ring is placed in xy plane where a uniform electric field exists $\overrightarrow{E}=E_0\hat{i}$

Find the work required to be done by external agent to rotate the ring about $z$ axis by $90°$ in clockwise direction.

Consider a metallic sphere of radius $R$ concentric with another hollow metallic sphere of inner radius $2R$ and outer radius $3R$ as shown in the figure. The inner,sphere is given a charge $-Q$ and outer $+2Q$. The electrostatic potential energy of the system is

An electric dipole lies in an electric field $\overrightarrow{E}=1000\hat{i} \mathrm{N}/\mathrm{C}$ in such a position that its dipole moment is $(12\hat{i}+5\hat{j})\times {10}^{-29}\mathrm{C}-\mathrm{m}.$ It is rotated so that the dipole moment becomes $(-12\hat{i}+5\hat{j})\times {10}^{-29}\mathrm{C}-\mathrm{m}.$ The work done by the external agent 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?

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 wooden block performs SHM on a frictionless surface with frequency $v_0.$ The block carries a charge $+Q$ on its surface. If now a uniform electric field $\overrightarrow{E}$ is switched on as shown in the figure given below, then the SHM of the block will be