Electric Dipole

Interactive Feed

JEE Main 2019

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

\frac{F}{3}

(B)

3 F

(C)

9 F

(D)

27 F

JEE Main 2017

LEVELJEE Main

An electric dipole has a fixed dipole moment $p$ , which makes angle $θ$ with respect to X-axis. When subjected to an electric field $E_{1} = E \hat{i}$ , it experiences a torque $T_{1} = τ \hat{k}$ . When subjected to another electric field $E_{2} = 3 E \hat{j}$ , it experiences a torque $T_{2} = - T_{1}$ . The angle $θ$ is

(A)

4 5^{\circ}

(B)

6 0^{\circ}

(C)

9 0^{\circ}

(D)

3 0^{\circ}

LEVELJEE Main

An electric dipole is placed at an angle of $3 0^{\circ}$ to a non-uniform electric field. The dipole will experience

(A)

a translational force only in the direction of the field

(B)

a translational force only in a direction normal to the direction of the field

(C)

a torque as well as a translational force

Two identical electric point dipoles have dipole moments $p_{1} = p \hat{i}$ and $p_{2} = - p \hat{i}$ 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)

\frac{p}{a} \frac{1}{π ϵ _{0} ma}

(B)

\frac{p}{a} \frac{1}{2 π ϵ _{0} ma}

(C)

\frac{p}{a} \frac{2}{π ϵ _{0} ma}

(D)

\frac{p}{a} \frac{3}{2 π ϵ _{0} ma}

JEE Main 2020

LEVELJEE Main

An electric dipole of moment $p = (- \hat{i} - 3 \hat{j} + 2 \hat{k}) \times 1 0^{- 29}$ C-m is at the origin (0, 0, 0). The electric field due to this dipole at $r = + \hat{i} + 3 \hat{j} + 5 \hat{k}$ (note that $r \cdot p = 0$ ) is parallel to

(A)

(+ \hat{i} - 3 \hat{j} - 2 \hat{k})

(B)

(- \hat{i} - 3 \hat{j} + 2 \hat{k})

(C)

(+ \hat{i} + 3 \hat{j} - 2 \hat{k})

(D)

(- \hat{i} + 3 \hat{j} - 2 \hat{k})

JEE Main 2019

LEVELJEE Main

Two electric dipoles, $A, B$ with respective dipole moments $d_{A} = - 4 q a \hat{i}$ and $d_{B} = - 2 q a \hat{i}$ 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

(A)

\frac{2 R}{2 + 1}

(B)

\frac{2 R}{2 - 1}

(C)

\frac{R}{2 + 1}

(D)

\frac{R}{2 - 1}

JEE Main 2019

LEVELJEE Main

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

(A)

3 q l \frac{j ^ - i ^}{2}

(B)

2 q l \hat{j}

(C)

- 3 q l \hat{j}

(D)

(q l) \frac{i ^ + j ^}{2}

JEE Main 2021

LEVELJEE Advanced

An electric dipole is placed on X-axis in proximity to a line charge of linear charge density $3.0 \times 1 0^{- 6}$ 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 4 N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

μ

μ

LEVELJEE Main

Two point charges $+ q$ and $- q$ are held fixed at $(- d, 0)$ and $(d, 0)$ respectively of a $x$ - $y$ co-ordinate system. Then

(A)

the electric field

E

at all points on the

x

-axis has the same direction.

(B)

work has to be done in bringing a test charge from

\infty

to the origin.

(C)

electric field at all point on

y

-axis is along

x

-axis.

(D)

the dipole moment is

2 q d

along the

x

-axis.

JEE Advanced 2003

LEVELJEE Advanced

A positive point charge $q$ is fixed at origin. A dipole with a dipole moment $p$ is placed along the $x$ -axis far away from the origin with $p$ pointing along positive $x$ -axis. Find : (a) the kinetic energy of the dipole when it reaches a distance $d$ from the origin, and (b) the force experienced by the charge $q$ at this moment.

JEE Advanced 2026

LEVELJEE Advanced

Consider an electric dipole comprising two charges $+ q$ and $- q$ each with mass $m$ , separated by a fixed distance $d$ and initially at rest with its dipole moment pointing along $\hat{i}$ . A uniform electric field $E \hat{j}$ is turned on at time $t = 0$ and it is turned off at $t = t_{f}$ , when the dipole moment makes an angle $θ_{f}$ with $\hat{i}$ . Neglecting any sources of energy loss, correct option(s) is/are:

* Multiple Correct Options

(A)

The center of mass of the dipole is deflected towards

\hat{j}

in the presence of the field.

(B)

If the magnitude of the final angular velocity

ω_{f} = \frac{2 q E}{m d}

then

θ_{f} = \frac{π}{6}

(C)

θ_{f} = π /4

, then the change in kinetic energy of the dipole is given by

23 q E d

(D)

For

θ_{f} = π /4

, the dipole rotates around its center of mass with a constant angular velocity after

t > t_{f}

JEE Advanced 2023

LEVELJEE Main

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

(A)

V_{0} /4

(B)

V_{0} /2

(C)

V_{0} / 2

(D)

3 V_{0} /4

JEE Main 2025

LEVELJEE Advanced

List-I shows four configurations, each consisting of a pair of ideal electric dipoles. Each dipole has a dipole moment of magnitude $p$ , oriented as marked by arrows in the figures. In all the configurations the dipoles are fixed such that they are at a distance $2 r$ apart along the $x$ direction. The midpoint of the line joining the two dipoles is $X$ . The possible resultant electric fields $E$ at $X$ are given in List-II. Choose the option that describes the correct match between the entries in List-I to those in List-II.

List-I

List-II

(1)

E = 0

(2)

E = - \frac{p}{2 π ϵ _{0} r ^{3}} \hat{j}

(3)

E = - \frac{p}{4 π ϵ _{0} r ^{3}} (\hat{i} - \hat{j})

(4)

E = \frac{p}{4 π ϵ _{0} r ^{3}} (2 \hat{i} - \hat{j})

(5)

E = \frac{p}{π ϵ _{0} r ^{3}} \hat{i}

JEE Advanced 2020

LEVELJEE Advanced

A point charge $q$ of mass $m$ is suspended vertically by a string of length $l$ . A point dipole of dipole moment $p$ 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 $N \times (m g h)$ , 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, $\frac{F}{s i n θ}$ is the same for all forces, where $F$ is any one of the forces and $θ$ is the angle between the other two forces)

JEE Advanced 2024

LEVELJEE Advanced

A small electric dipole $p_{0}$ , having a moment of inertia $I$ about its center, is kept at a distance $r$ from the center of a spherical shell of radius $R$ . The surface charge density $σ$ is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle $θ$ as shown in the figure. While staying at a distance $r$ , the dipole is free to rotate about its center. If released from rest, then which of the following statement(s) is(are) correct? [ $ε_{0}$ is the permittivity of free space.]

* Multiple Correct Options

(A)

The dipole will undergo small oscillations at any finite value of

r

(B)

The dipole will undergo small oscillations at any finite value of

r > R

(C)

The dipole will undergo small oscillations with an angular frequency of

\frac{2 σ p _{0}}{ε _{0} I}

r = 2 R

(D)

The dipole will undergo small oscillations with an angular frequency

\frac{σ p _{0}}{100 ε _{0} I}

r = 10 R

JEE Advanced 2019

LEVELJEE Advanced

An electric dipole with dipole moment $p_{0} = \frac{p _{0}}{2} (\hat{i} + \hat{j})$ is held fixed at the origin O in the presence of an uniform electric field of magnitude $E_{0}$ . If the potential is constant on a circle of radius R centered at the origin as shown in figure, then the correct statement(s) is/are: ( $ε_{0}$ is permittivity of free space, $R >>$ dipole size)

* Multiple Correct Options

(A)

R = (\frac{p _{0}}{4 π ε _{0} E _{0}})^{1/3}

(B)

The magnitude of total electric field on any two points of the circle will be same

(C)

Total electric field at point A is

E_{A} = 2 E_{0} (\hat{i} + \hat{j})

(D)

Total electric field at point B is

E_{B} = 0

JEE Main 2019

LEVELJEE Main

An electric field of 1000 V/m is applied to an electric dipole at angle of $4 5^{\circ}$ . The value of electric dipole moment is $1 0^{- 29}$ C-m. What is the potential energy of the electric dipole?

(A)

- 9 \times 1 0^{- 20}

(B)

- 10 \times 1 0^{- 29}

(C)

- 20 \times 1 0^{- 18}

(D)

- 7 \times 1 0^{- 27}

JEE Main 2019

LEVELJEE Main

A point dipole $p = - p_{0} \hat{x}$ 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]

(A)

\frac{∣ p ∣}{4 π ε _{0} d ^{2}}, \frac{p}{4 π ε _{0} d ^{3}}

(B)

0, \frac{- p}{4 π ε _{0} d ^{3}}

(C)

0, \frac{p}{4 π ε _{0} d ^{3}}

(D)

\frac{∣ p ∣}{4 π ε _{0} d ^{2}}, \frac{- p}{4 π ε _{0} d ^{3}}

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } An electric dipole is placed at an angle of 30∘ to a non-uniform electric field. The dipole will experience

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

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two point charges +q and −q are held fixed at (−d,0) and (d,0) respectively of a x-y co-ordinate system. Then

List-I

List-II

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A point dipole p=−p0​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]

An electric dipole is placed at an angle of $3 0^{\circ}$ to a non-uniform electric field. The dipole will experience

Two point charges $+ q$ and $- q$ are held fixed at $(- d, 0)$ and $(d, 0)$ respectively of a $x$ - $y$ co-ordinate system. Then

A point dipole $p = - p_{0} \hat{x}$ 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]