Electric Dipole

The S.I unit of electric dipole moment is

Which orientation of an electric dipole(p) in a uniform electric field(E) would correspond to stable equilibrium?

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 moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta =90^{\text{o}}$, the torque and the potential energy of the dipole will respectively be

Assertion (A): An electric dipole is placed in a uniform electric field. Its equilibrium will be stable when the dipole is set along the direction of the electric field.

Reason (R): In stable equilibrium energy of dipole should be the least possible.

Assertion (A):  An electric dipole is placed in a uniform electric field. Its equilibrium will be stable when the dipole is set along the direction of the electric field.

Reason (R): In stable equilibrium energy of dipole should be the least possible.

For unstable equilibrium, basic two conditions are (what should be angle between $\overrightarrow{\mathrm{P}} \& \overrightarrow{\mathrm{E}}$ and $\mathrm{U}$)

When electric dipole is kept in uniform electric field such that torque is zero and potential energy is maximum then equilibrium is

If an electric dipole is placed in a uniform electric field ______ will act on the dipole.

A dipole is said to be in stable equilibrium when angle between electric field and dipole moment is:​

If an electric dipole is kept on the axis of a uniformly charged ring at distance $\frac{R}{\sqrt{2}}$ from the centre of the ring. The direction of the dipole moment is along the axis of the ring. The dipole moment is $P$, charge of the ring is $Q$and radius of the ring is $R$. The force on the dipole is

Electric field on the axis of a small electric dipole at a distance $r$ is $\overrightarrow{E_1}$ and $\overrightarrow{E_2}$ at a distance of $2r$ on a line of perpendicular bisector. Then

Choose the correct statement.

A tiny electric dipole ($H_{2}O$ molecule) of dipole moment $\overrightarrow{p}$ is placed at a distance $r$ form an infinitely long wire, with its $\overrightarrow{p}$ normal to the wire in the same plane. If the linear charge density of the wire is $\lambda ,$ the electrostatic force acting on the dipole is equal to $\frac{\lambda p}{W\pi {\epsilon }_0{r}^K}$. Obtain the value of $(W+K).$

The dipole moment of a system of charge $+q$ distributed uniformly on an arc of radius $R$ subtending an angle $\pi /2$ at its centre where another charge $-q$ is placed is $x \mathrm{C} \mathrm{m}$. Find the value of $x$. Given $\left(q=1 \mathrm{C}, R=\sqrt{8}\pi m\right)$

Three short electric dipoles, each of dipole moment $P\mathit{,}$ are placed at the vertices of an equilateral triangle of side length $L\mathit{.}$ Each dipole has its moment, oriented parallel to the opposite side of the triangle as shown in the fig. The electric field strength at the centroid of the triangle is $\sqrt{a}\frac{KP}{L^3}.$ Then value of $a$ is :

A point charge $q$ of mass $m$ is suspended vertically by a string of length $\ell .$ A point dipole of dipole moment $\overrightarrow{p}$ is now brought towards $q$ from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is $N\times \left(mgh\right),$ where $g$ is the acceleration due to gravity, then the value of $N$ is (Note that for three coplanar forces keeping a point mass in equilibrium, $\frac{F}{\sin \theta }$ is the same for all forces, where $F$ is any one of the forces and $\theta$ is the angle between the other two forces) 

The electric potential at the equatorial position due to the dipole is zero.

Calculate the electric field due to a dipole at a point on the equatorial plane.

An electric dipole of length $1 \mathrm{cm}$ is placed with the axis making an angle of $30°$ to an electric field of strength ${10}^4 \mathrm{N} {\mathrm{C}}^{-1}$. If it experiences a torque of $10\sqrt{3} \mathrm{N} \mathrm{m}$, the potential energy (in joule) of the dipole is $-x \mathrm{J}$. Find the value of $x$.