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?

An electric dipole is formed by two charges $+q$ and $-q$ located in $xy$-plane at $(0, 2) \mathrm{mm}$ and $(0, -2) \mathrm{mm}$, respectively, as shown in the figure. The electric potential at point $P(100, 100) \mathrm{mm}$ due to the dipole is $V_0$. The charges $+q$ and $–q$ are then moved to the points $(-1, 2) \mathrm{mm}$ and $(1, -2) \mathrm{mm}$, respectively. What is the value of electric potential at $P$ due to the new dipole?

A small dipole of dipole moment $p$ is placed at a distance $2R$ from the centre of a neutral conducting sphere of radius $R.$ The direction of dipole is towards the centre of the sphere. A tangent is drawn from the centre of dipole to the sphere which meets the sphere at point $A.$

An electric dipole moment $\overrightarrow{p}=(2.0\hat{i}+3.0\hat{j}) \mathrm{\mu m} \mathrm{C}.$ It is placed in a uniform electric field $\overrightarrow{E}=(3.0\hat{i}+2.0\hat{k})\times {10}^5 \mathrm{N} {\mathrm{C}}^{-1}$

Two identical dipoles of dipole moment $P=p_0\hat{i}\left(p_0\right.$ is a positive constant) are placed on $x-$axis at points $A(a, 0, 0)$ and $B(-a, 0, 0)$ as shown. Then pick up the correct statements:

Given square frame of diagonal length $2r$$2 r$ made of insulating wires. There is a short ideal electric dipole, having dipole moment $P$, fixed in the plane of the figure lying at the centre of the square, making an angle $\theta$ as shown in figure. four identical particles having charges of magnitude $q$ each and alternatively positive and negative are placed at the four corners of the square. Select the correct alternative(s). (neglect gravitationa effects) $\left(k=\frac{1}{4\pi {\epsilon }_0}\right)$ (Centre of dipole coincidence with the intersecting point of diagonals)

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

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 $x$.

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:

An electric dipole is formed by two equal and opposite charges $\mathrm{q}$ with separation $\mathrm{d}$. The charges have same mass $\mathrm{m}$. It is kept in a uniform electric field $\mathrm{E}$. If it is slightly rotated from its equilibrium orientation, then its angular frequency to is :

An electric dipole is placed in a uniform electric field. Assuming the angle between the electric field and dipole axis is $45°$, the dipole will experience