Electric Dipole

Three charges $+2q, +3q$ and $-4q$ are situated at $(0, -3a), (2a, 0)$ and $(-2a, 0)$ respectively in the $xy$ plane. The resultant dipole moment about origin is ______.

A dipole of electric dipole moment $\vec{P}$ is placed in an electric field of strength $\vec{E}$. The angle between $\vec{P}$ and $\vec{E}$ for which the potential energy of the electric dipole is maximum, is

An electric dipole of length $3$cm is placed with its axis making an angle of $60^\circ$ with a uniform electric field of $5 \times 10^{4}$N/C. It experiences a torque of $9\sqrt{3}$ Nm. The magnitude of charge on the dipole is $\left(\sin 60^\circ = \frac{\sqrt{3}}{2}\right)$

An electric dipole of length $0.5\,\mu$m is placed with its axis making an angle of $30^\circ$ with uniform electric field $10^{4}$ V/m. If it experiences a torque of $5 \times 10^{-9}$ Nm, the magnitude of the charge on the dipole is ($\sin 30^\circ = 0.5$)

Polar molecules are those in which

When a dielectric is placed in an electric field, the electric field inside the dielectric

When the dielectric is placed in an external electric field, the electric field inside the dielectric is

Select the 'WRONG' statement about polar molecules.

Select the WRONG statement about polar molecules.

When a dipole placed parallel to electric field is rotating through $\pi^c$, the work done is W. The work done in rotating the dipole through $\left(\frac{\pi}{3}\right)^c$ is

($\cos 0^\circ = 1,\ \cos 60^\circ = \frac{1}{2},\ \cos 180^\circ = -1$)

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\vec{E}_1 = E_0\hat{x}$. If another electric field $\vec{E}_2 = 2E_0(\hat{y} + \hat{z})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

Two electric dipoles of moment $P$ and $8P$ are placed in opposite directions on a line at a distance of $24$ cm. The electric field will be zero at the point between the dipoles whose distance from the dipole of moment $P$ will be $x_1$. When $8P$ is replaced by $27P$ keeping all other quantities the same, the distance $x_1$ now becomes $x_2$. The difference $|x_2 - x_1|$ is ( All the distances are measured from the centers of the dipole.)

Two short electric dipoles A and B having dipole moment $p_1$ and $p_2$ respectively are placed with their axes mutually perpendicular as shown in the figure. The resultant electric field at a point $x$ is making an angle of $60^\circ$ with the line joining points $O$ and $x$. The ratio of the dipole moments $p_2/p_1$ is _________.

Two short dipoles $(A, B), A$ having charges $\pm 2\,\mu\text{C}$ and length 1 cm and $B$ having charges $\pm 4\,\mu\text{C}$ and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point $P$, equi-distant from the centres of both dipoles is ______ N/C.

An electric dipole of length 2 cm is placed with its axis making an angle of $60^\circ$ to a uniform electric field of $10^{+5}\text{ N/C}$. If it experiences a torque of $9\sqrt{3}\text{ Nm}$, the magnitude of the charge on the dipole is $\left(\sin 60^\circ = \frac{\sqrt{3}}{2}\right)$

An electric dipole having each charge of magnitude $2\mu\text{C}$ is placed in an electric field of intensity $8 \times 10^{+4}\text{ N/C}$. If the maximum torque acting on the dipole is $4 \times 10^{-3}\text{ N-m}$, the length of the dipole is

An electric dipole of dipole moment ' $p$ ' is aligned parallel to a uniform electric field ' E '. The energy required to rotate the dipole by $90^\circ$ is $\left[\begin{matrix}\sin 0^\circ = 0, & \sin 90^\circ = 1 \\ \cos 0^\circ = 1, & \cos 90^\circ = 0\end{matrix}\right]$

An electric dipole with dipole moment $5 \times 10^{-6}\text{ Cm}$ is aligned with the direction of a uniform electric field of magnitude $4 \times 10^{5}\text{ N/C}$. The dipole is then rotated through an angle of $60^\circ$ with respect to the electric field. The change in the potential energy of the dipole is:

A dipole with two electric charges of 2 µC magnitude each, with separation distance 0.5 µm, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30° from the axis, it tends to realign in the direction due to a torque. The value of torque is:

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density $\sigma_0$. Choose the correct option from the following.

Two point charges $-4\,\mu\text{C}$ and $4\,\mu\text{C}$, constituting an electric dipole, are placed at $(-9, 0, 0)\text{ cm}$ and $(9, 0, 0)\text{ cm}$ in a uniform electric field of strength $10^{4}\text{ NC}^{-1}$. The work done on the dipole in rotating it from the equilibrium through $180^\circ$ is:

An electric dipole of dipole moment $6 \times 10^{-6}\text{ Cm}$ is placed in uniform electric field of magnitude $10^{6}\text{ V/m}$. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be _______ J.

Out of the following molecules the one which represents the polar molecule is

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.

Reason (R): In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.

In the light of the above statements, choose the most appropriate answer from the options given below:

For a short dipole placed at origin O, the dipole moment P is along $x$-axis, as shown in the figure. If the electric potential and electric field at $A$ are $V_0$ and $E_0$, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the $y$-axis is given by

Two small spherical balls of mass 10 g each with charges $-2\,\mu\text{C}$ and $2\,\mu\text{C}$, are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of $100\,\mu\text{C/m}^2$ such that length of rod makes an angle of $30^\circ$ with electric field generated by charge sheet. Net torque acting on the rod is: (Take $\varepsilon_0 : 8.85 \times 10^{-12}\text{ C}^2/\text{Nm}^2$)

An electric dipole of mass $m$, charge $q$, and length $l$ is placed in a uniform electric field $\vec{E} = E_0\hat{i}$. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

A point particle of charge $Q$ is located at $P$ along the axis of an electric dipole 1 at a distance $r$ as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charge q separated by a distance $2a$. For the charge particle at P not to experience any net force, which of the following correctly describes the situation?

The electric potential at a point on the axis of an electric dipole is proportional to [r = distance between centre of the electric dipole and the point]

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: The potential (V) at any axial point, at $2\text{ m}$ distance $(r)$ from the centre of the dipole of dipole moment vector $\vec{P}$ of magnitude, $4 \times 10^{-6}\text{ Cm}$, is $\pm 9 \times 10^{3}\text{ V}$.

(Take $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ SI}$ units)

Reason R: $V = \pm\frac{2P}{4\pi\epsilon_0 r^2}$, where $r$ is the distance of any axial point, situated at $2\text{ m}$ from the centre of the dipole.

In the light of the above statements, choose the correct answer from the options given below:

The electrostatic potential due to an electric dipole at a distance '$r$' varies as:

An electric dipole will have minimum potential energy when it subtends an angle $\begin{bmatrix} \cos 0^\circ = 1 \\ \sin 0^\circ = 0 \end{bmatrix} \begin{bmatrix} \cos 90^\circ = 0 \\ \cos \pi = -1 \end{bmatrix}$

When the dielectric is placed in an external electric field, the electric field inside the dielectric is

The electric field at point $P$ due to an electric dipole is $E$. The electric field at point $R$ on equatorial line will be $\frac{E}{x}$. The value of $x$:

The distance between charges $+q$ and $-q$ is $2l$ and between $+2q$ and $-2q$ is $4l$. The electrostatic potential at point $P$ at a distance $r$ from center $O$ is $-\alpha \left[\frac{ql}{r^2}\right] \times 10^{9}\text{ V}$, where the value of $\alpha$ is __________. (Use $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}\text{ Nm}^2\text{C}^{-2}$)

An electric dipole of moment$\vec{p}$is lying along a uniform electric field $\vec{E}$. The work done in rotating the dipole through $\frac{\pi^c}{3}$ is $\left[\sin 30^\circ = \cos 60^\circ = 0.5,\ \cos 30^\circ = \sin 60^\circ = \sqrt{3}/2\right]$

Two charges of $-4\,\mu\text{C}$ and $+4\,\mu\text{C}$ are placed at the points $A(1, 0, 4)\text{ m}$ and $B(2, -1, 5)\text{ m}$ located in an electric field $\vec{E} = 0.20\hat{i}\text{ V/cm}$. The magnitude of the torque acting on the dipole is $8\sqrt{\alpha} \times 10^{-5}\text{ Nm}$, where $\alpha =$ _________.

If $E_a$ and $E_q$ represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance '$r$' from the centre of the dipole, then

The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as:

An electric dipole consisting of two opposite charges of $2 \times 10^{-6}\text{ C}$ separated by a distance of $3\text{ cm}$ placed in an electric field of $2 \times 10^{5}\text{ N/C}$ then the maximum torque acting on dipole is

An electric dipole is placed at an angle of $30^\circ$ with an electric field of intensity $2 \times 10^{5}\text{ NC}^{-1}$. It experiences a torque equal to $4\text{ N m}$. Calculate the magnitude of charge on the dipole, if the dipole length is $2\text{ cm}$.

Two charges each of magnitude $0.01\text{ C}$ and separated by a distance of $0.4\text{ mm}$ constitute an electric dipole. If the dipole is placed in an uniform electric field '$\vec{E}$' of 10 dyne/C making $30^\circ$ angle with $\vec{E}$, the magnitude of torque acting on dipole is:

An electric dipole of dipole moment $6.0 \times 10^{-6}\text{ Cm}$ is placed in a uniform electric field of $1.5 \times 10^{3}\text{ NC}^{-1}$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $180^\circ$ in this field will be ___________ $\text{mJ}$.

If the magnitude of intensity of electric field at a distance '$r_1$ ' on an axial line and at a distance '$r_2$ ' on an equatorial line due to a given short dipole are equal, then $r_1 : r_2$, is

An electric dipole is placed as shown in the figure.

The electric potential (in 102 V) at point P due to the dipole is ($\epsilon_0$ = permittivity of free space and $\frac{1}{4\pi\epsilon_0}$ = K):

The work done in rotating a dipole placed parallel to the electric field through $180^\circ$ is W. So, the work done in rotating it through $60^\circ$ is $\left(\cos 0^\circ = 1,\ \cos 60^\circ = \frac{1}{2},\ \cos 180^\circ = -1\right)$

Two electric dipoles of moment $P$ and $27P$ are placed on a line with their centres $24\text{ cm}$ apart. Their dipole moments are in opposite direction. At which point the electric field will be zero between the dipoles from the centre of dipole of moment P?

A dipole comprises of two charged particles of identical magnitude $q$ and opposite in nature. The mass 'm' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance '$l$'. If the dipole is placed in a uniform electric field '$\vec{E}$'; in such a way that dipole axis makes a very small angle with the electric field, '$\vec{E}$'. The angular frequency of the oscillations of the dipole when released is given by:

Two point charges $-$q and +q are placed at a distance of L, as shown in the figure.

The magnitude of electric field intensity at a distance R(R >> L) varies as:

Two electric dipoles of dipole moments $1.2 \times 10^{-30}\text{ Cm}$ and $2.4 \times 10^{-30}\text{ Cm}$ are placed in two different uniform electric fields of strengths $5 \times 10^{4}\text{ NC}^{-1}$ and $15 \times 10^{4}\text{ NC}^{-1}$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $\frac{1}{x}$. The value of $x$ is __________.

Given below two statements: One is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A): Non-polar materials do not have any permanent dipole moment. Reason (R): When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution.

In the light of above statements, choose the most appropriate answer from the options given below.

An electric dipole having dipole moment $\mathrm{P} = \mathrm{q} \times 2\ell$ is placed in a uniform electric field '$\mathrm{E}$'. The dipole moment is along the direction of the field. The force acting on it and its potential energy are respectively

A dipole is placed in an electric field as shown. In which direction will it move?

Polar molecules are the molecules:

Two ideal electric dipoles A and B, having their dipole moment p1 and p2 respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37$^\circ$ with the axis. The ratio of the dipole moment of A and B, $\frac{p_1}{p_2}$ is: (take $\sin 37^\circ = \frac{3}{5}$)

An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 $\times$ 10 $-$6 C/m. Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. If total force of 4N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

The electric field at a point on the equatorial plane at a distance $r$ from the centre of a dipole having dipole moment $\vec{p}$ is given by,

($r \gg$ separation of two charges forming the dipole, $\varepsilon_0$ - permittivity of free space)

A short electric dipole has a dipole moment of 16 $\times$ 10-9 Cm. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of $60^\circ$ with the dipole axis is:

$\left(\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}\text{ Nm}^2/\text{C}^2\right)$

An electric dipole of moment

$\vec{p} = \left(-\hat{i} - 3\hat{j} + 2\hat{k}\right) \times 10^{-29}$ C.m is

at the origin (0, 0, 0). The electric field due to this dipole at

$\vec{r} = +\hat{i} + 3\hat{j} + 5\hat{k}$ (note that$\vec{r} \cdot \vec{p} = 0$) is parallel to:

Two identical electric point dipoles have dipole moments $\vec{p}_1 = p\hat{i}$ and $\vec{p}_2 = -p\hat{i}$ and are held on the x axis at distance '$a$' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is:

A point dipole $\vec{p} = -p_0\hat{x}$ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: (Take V= 0 at infinity)

Determine the electric dipole moment of the system of the three charges, placed on the vertices of an equilateral triangle, as shown in the figure:

An electric field of 1000 V/m is applied to an electric dipole at angle of 45o. The value of electric dipole moment is 10–29 C.m. What is the potential energy of the electric dipole?

Which of the following is the dimensional formula for electric polarisation?

Which of the following molecules is a polar molecule?

Charges –q and +q located at A and B, respectively, constitude an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to P' such that OP' = $\left(\frac{y}{3}\right)$, the force on Q will be close to - $\left(\frac{y}{3} \gg 2a\right)$

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

Two electric dipoles, A, B with respective dipole moments $\vec{d}_A = -4qa\hat{i}$ and $\vec{d}_B = -2qa\hat{i}$ are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is -

An electric dipole has a fixed dipole moment $\vec{p}$, which makes angle $\theta$ with respect to x-axis. When subjected to an electric field $\vec{E}_1 = E\hat{i}$, it experiences a torque $\vec{T}_1 = \tau\hat{k}$. When subjected to another electric field $\vec{E}_2 = \sqrt{3}E_1\hat{j}$ it experiences a torque $\vec{T}_2 = -\vec{T}_1$. The angle $\theta$ is:

An electric dipole is placed at an angle of 30o with an electric field intensity 2 $\times$ 105 N C${}^{-1}$. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is

An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90o is

Two point dipoles of dipole moment $\vec{p}_1$ and $\vec{p}_2$ are at a distance x from each other and $\vec{p}_1 \parallel \vec{p}_2$. The force between the dipoles is:

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 $\theta$ = 90o, the torque and the potential energy of the dipole will respectively be

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

An electric dipole is placed at an angle of $30^\circ$ to a non-uniform electric field. The dipole will experience

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

A dipole of dipole moment $\vec{p}$is placed in uniform electric field $\vec{E}$then torque acting on it is given by

A point $Q$ lies on the perpendicular bisector of an electrical dipole of dipole moment $p$. If the distance of $Q$ from the dipole is $r$ (much larger than the size of the dipole) then electric field at $Q$ is proportional to

An electric dipole of moment $p$ is placed in the position of stable equilibrium in uniform electric field of intensity $E$. This is rotated through an angle $\theta$ from the initial position. The potential energy of the electric dipole in the final position is