Electric Dipole - Definition, Formula, FAQs

Two charges, equal in magnitude, but opposite in sign separated by a small distance form a dipole. It is an elementary magnet whose positive end attracts negative ends while repelling positive ones; similarly, each side acts like a beginning and an end. Electric dipoles are essential for investigating how molecules interact since most of these compounds have such properties due to differences in their electron distribution between nuclei making them have a partial positive charge on one side while having partial negative charges on other angles of inclination towards this aspect instead if looked at it from different perspectives at the same time it makes it appear both as positive and negative but since they are near each other from the point at which we stand there is no way they could be seen. A torque is exerted on the dipole by the electric field; this torque tends to align the dipole with the field.

An electric dipole is a key concept in electrostatics that is essential for understanding how electric fields and potentials work. Better-skilled individuals find it easier when it comes to problem-solving in the electric field, potential energy calculations or even determining dipoles’ torques under uniform electric fields during NEET and JEE Main exams. Over the last ten years of the JEE Main exam (from 2013 to 2023), a total of five questions have been asked on this concept. And for NEET one question was asked from this concept.

What is an Electric Dipole?
A pair of opposite charges q and –q separated by a distance d is called an electric dipole. Electric dipoles in space always point from negative charge -q to positive charge q by default. The dipole's center is defined as the point where q and –q meet. A pair of electric charges with opposite signs and equal magnitude separated by distance is the simplest example of an electric dipole.

(Electric dipole field of two point charges)

There are two types of dipoles in electromagnetism: In every electromagnetic system, an electric dipole is used to separate the positive and negative charges. A pair of electric charges of equal magnitude but opposite sign separated by a typically small distance is a simple example of this system.

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Electric Dipole Visualization-

Assume there are two equal-sized charges, ‘q,' separated by a distance, d. An electric dipole is the name given to this configuration. As a result, we can state that an electric dipole is formed by a separation of a specific distance between equal and opposite charges.

The symbol p stands for an electric dipole. The product of the magnitude of the charges multiplied by the distance between them is known as an electric dipole, and it may be mathematically stated as follows:

An electric dipole's magnitude is expressed as ,

p = Qd.

Direction of electric dipole moment-

The electric dipole moment is a vector quantity with a definite direction of travel from negative to positive charge. It's vital to remember, however, that this orientation norm is solely followed in Physics. In chemistry, the convention is that the polarity should be reversed, from positive to negative. The axis of the dipole is the line that runs along the direction of an electric dipole.

Electric potential due to dipole-

The dipole moment of an electric dipole is given by the formula P=2qa. V=Kqr denotes the electric potential owing to a charge q at a position r away from the charge, where V denotes the charge's potential and K denotes the permittivity of free space.

Due to a Dipole, there is an electric potential (V)

Assume that a dipole is formed by two charges, –q at A and +q at B, separated by a distance d. Assume that O is the midpoint of AB.

At every location P where OP = r, the electric potential due to a dipole will be:

V= P cosθ/4πϵ r²

If = 90°, this is the first case.

V = 0 is the electric potential.

Case 2: If is equal to 0°

V= P/4πϵ r²

= electric potential

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Electric Dipole formula-

For a pair of equal and opposing charges, the formula for electric dipole moment is p = qd, where qd is the magnitude of the charges multiplied by the distance between them.

Electric Dipole Moment-

The Electric Dipole moment is a measurement of a system's overall polarity or the separation of positive and negative electrical charges inside it. The coulomb-meter (Cm) is the SI unit for electric dipole moment; nevertheless, the debye is a regularly used unit in atomic physics and chemistry (D).

Example of Electric Dipole-

A pair of electric charges with opposite signs and equal magnitude separated by distance is the simplest example of an electric dipole.

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Force between two dipoles-

The potential energy of two electric dipoles determines the force operating between them. Because the charges are pushed equally and oppositely when the dipole moment is constant, the net force is zero.

Dipole’s physical importance that is its significance-

The Electric Dipole is important in both electrostatics and chemistry. Because the centres of positive and negative charges in most molecules occur at the same place, the distance between two charges is zero. Carbon dioxide and methane belong to the zero dipole moment category. Non-polar molecules are the name for this sort of molecule. Polar molecules are those that have a persistent dipole moment because the centres of positive and negative charge do not coincide.

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Solved Examples Based On Electric Dipole

Example 1: An electric dipole is placed in an electric field generated by a point charge

1) The net electric force on the dipole must be zero

2) The net electric force on the dipole may be zero

3) The torque on the dipole due to the field must be zero

4) The torque on the dipole due to the field may be zero

Solution:

Electric dipole

Two equal and opposite charges are separated by a small distance.

wherein

Point charge produces a non-uniform electric field

Example 2: A point dipole p→=−p0x^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)
1) 0,−p→4πϵ0d3
2) 0,p→4πϵ0d3
3) |p→|4πϵ0d2,−p→4πϵ0d3
4) |p→|4πϵ0d2,p→4πϵ0d3

Solution:

V=0E=−kp→r3E→=−p→4πϵ0d3

Example 3: Shown in the figure is a shell made of a conductor. It has an inner radius a and outer radius b, and carries charge Q, At its centre is a dipole p→ as shown. In this case :

1) surface charge density on the outer surface depends on |p→|
2) The electric field outside the shell is the same as that of a point charge at the centre of the shell
3) surface charge density on the inner surface is uniform and equal to

(Q/2)4πa2

4) surface charge density on the inner surface of the shell is zero everywhere

Solution:

The charge distribution at equilibrium on the conductor will be like :

The net charge on the outer surface =Q
The total charge on the inner surface =0
If we take a Gaussian surface outside the shell.
So net charge inside the Gaussian surface will be Q .
So far any observed outside the shell, the resultant electric field is due to Q uniformly distributed on the outer surface and it is equal to

E=KQr2

So electric field outside the shell is the same as that of a point charge at the centre of the shell.

Example 4: Two charges +3.2∗10−19 and −3.2∗10−19C placed at 2.4 A apart from an electric dipole. It is placed in a uniform electric field of intensity 4∗105volt/m. The electric dipole moment is
1) 15.36∗10−29 coulomb ×m
2) 15.36∗10−19 coulomb ×m
3) 7.68∗10−29 coulomb ×m
4) 7.68∗10−19 coulomb ×m

Solution:

Dipole moment

(P→)=q(2l→)

Its S.I unit is C-m
and its CGS unit is Debye ( 1 Debye =3.3×10−30C−m )
Dipole moment p=q(2I)

=3.2×10−19×(2.4×10−10)=7.68×10−29Cm

Hence, the answer is the option (3).

Example 5: Two opposite and equal charges 4×10−8 when placed 2×10−2 away, form a dipole. If this dipole is placed in an external electric field 4×10−8, the value of maximum torque and the work done in rotating it through 180∘ will be
1) 64×10−4Nm.. and.. 64×10−4 J
2) 32×10−4Nm.. and.. 32×10−4J
3) 64×10−4Nm.. and.. 32×10−4J
4) 32×10−4Nm.. and.. 64×10−4J

Solution:

Dipole moment

(P→)=q(2l→)

S.I unit - C-m or Debye

1 Debye =3.3×10−30c−m

- wherein

2l→ dipolelength

Dipole moment p=4∗10−8∗2∗10−4=8∗10−12 m
Maximum torque =pE=8∗10−12∗4∗108

=322∗10−4Nm

Work done in rotating through 180∘=2pE

=2∗32∗10−4=64∗10−4 J

Hence, the answer is the option (4).

Summary

The electric dipole is made up of two same charges which are oppositely and a small distance at that point separates them. It therefore has a property known as its dipole moment; this is a vector which points from the negative end of the charge to the positive end of the charge across a separation. A dipole which was at rest in space will develop torque under the influence of external electric field forces applied to it with the aim of making its axes align with these lines.