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

Two electric dipoles of moments $p$ and $27\mathrm{p}$ are placed in opposite direction on a line at a distance of $24 \mathrm{cm}.$ The electric field will be zero at a point between the dipoles whose distance from the dipole of moment $p$ is

An electric dipole is placed in a non-uniform electric field. Then net:

Two opposite charges each of magnitude $500 \mathrm{\mu c}$ are $10 \mathrm{cm}$ apart. Find electric field intensity at a distance of $25 \mathrm{cm}$ from the midpoint on axial line of the dipole.

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 $\left(q=1 \mathrm{C}, R=\sqrt{8}\pi m\right)$

Consider two spheres of the same radius $R$ having uniformly distributed volume charge density of same magnitude but opposite sign $(+\rho$ and $-\rho ).$ The spheres overlap such that the vector joining the centres of the negative sphere to that of the positive sphere is $\overrightarrow{d}\left(d\ll R\right).$The magnitude of the electric field at a point outside the spheres at a distance $r$ in a direction making an angle $\theta$ with $\overrightarrow{d}$ is found to be $\frac{\rho }{a\left({\epsilon }_0\right)}\left(\frac{R^{3}d}{r^3}\right)\sqrt{b{\cos }^2\theta +1}.$ The value of $(a+b)$ is (Distance $r$ is measured with respect to the mid point of the line joining the centers of the two spheres.)

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) 

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 $x$.

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.

If an electric dipole is placed in a uniform electric field, it experiences:

What is the unit of electric dipole moment?

Electric field due to the electric dipole at the equatorial plane is given as: