Electric Dipole: Definition, Significance and Electric Dipole Moment

Electric dipole is a pair of equal and opposite point charges +q and –q that are separated by a distance d. The line connecting the two charges defines a direction in space.

• Although it is considered that the direction from –q to q is the direction of the dipole.
• The midpoint of locations of –q and +q is called the center of the dipole.
• The simplest example of an electric dipole is a pair of electric charges with opposite signs having equal magnitude separated by a distance.

Key Terms: Electric dipole moment, Electric charge, Torque, Potential Energy, Electric fields, Electrostatic potential, Dipole length, Coulomb’s law

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Electric Dipole

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An electric dipole is a pair of equal and opposite charges separated by a certain distance. The center of an electric dipole is the midpoint of the line joining the two charges.

• The net charge of an electric dipole is zero since it is a pair of two equal and opposite charges.
• The electric field due to a dipole has some finite value because the two equal charges are separated by a certain distance.

An electric dipole having charges +q and -q separated by distance d, is shown in the figure below.

Electric Dipole

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What is Electric Dipole Moment?

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Dipole moment is generally known as the exact measure of the strength associated with an electric dipole. As per the studies based on the scientific and mathematical conclusions,

The dipole moment magnitude is the product of either of the charges that is a positive charge or the negative charge, and the separation distance denoted by (d) between them.

This also signifies that the dipole moment is a vector measure whose direction runs from a negative charge to a positive charge.

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Electric Dipole Moment Formula

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Let two charges +q and -q be separated by a distance d, the formula for the electric dipole moment for a pair of equal & opposite charges is

p = qd

Where,

• p is the Electric dipole moment
• q is the magnitude of the charge
• d is the distance between the two charges

Direction of Electric Dipole Moment

The electric dipole moment is a vector quantity having a definite direction from negative to positive charge. It is important to remember that this orientation norm or convention is only followed in Physics. In chemistry, the convention is that the polarity should be opposite, from positive to negative. The axis of the dipole refers to the line that runs along the direction of an electric dipole.

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Electric Field Due to an Electric Dipole

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The electric field due to a dipole is known as Dipole Field. It can be calculated by adding the electric field intensities due to both the charges of the dipole.

• Electric Field due to an Electric Dipole on the axial line (End-on position)

Consider an electric dipole of charge +q and -q having dipole moment p. The electric field intensity at distance r on the axial from the center of the dipole is given by

\(E = \frac {2p}{4\pi \epsilon_o r^3}\)

• Electric Field due to an Electric Dipole on the Equatorial line (Broad-side-on position)

Consider an electric dipole of charge +q and -q having dipole moment p. The electric field intensity at distance r on the axial from the center of the dipole is given by

\(E = \frac {p}{4\pi \epsilon_o r^3}\)

• Electric Field due to an Electric Dipole at any other point

Consider an electric dipole of charge +q and -q having dipole moment p. The electric field intensity at distance r and at an angle θ from the center of the dipole is given by

\(E = \frac {p \sqrt {1+3cos^2\theta}}{4\pi \epsilon_o r^3}\)

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Torque Experienced by an Electric Dipole in Uniform Electric Field

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Consider an electric dipole having charges +q and -q separated by distance 2l, placed in a uniform electric field E such that the dipole moment vector makes an angle of θ with the uniform electric field.

The negative charge experience a force F = -qE, in a direction opposite to the direction of the electric field.

The positive charge experience a force F = qE, in the direction of the electric field.

The net force acting on the dipole is F_net = -qE + qE = 0.

Hence, when an electric dipole is placed in a uniform electric field, it experiences zero net force.

The two forces form a couple and try to align the dipole in the direction of the electric field. The torque due to the couple is given by

Torque, τ = magnitude of either force x perpendicular distance between the two forces

⇒ τ = qE x AC

From ΔABC, we get AC = 2l sinθ

⇒ τ = qE x 2l sinθ

But 2ql = p (dipole moment)

⇒ τ = pE sinθ

Hence, torque experienced by an electric dipole in the uniform electric field is given by

\(\tau = pE sin \theta=\vec p\times \vec E\)

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Potential Energy Associated With an Electric Dipole

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Consider an electric dipole placed in an equilibrium position in a uniform electric field such that the angle between the electric dipole moment vector p and the electric field is 0 i.e. θ = 0^o. Now when the dipole is displaced from its equilibrium position to an angle θ, then the restoring torque experienced by the dipole is

τ = – pE sinθ

An electric dipole is associated with potential energy when placed in a uniform electric field. The change in potential energy (dU) is related to the work done (dW) by the electric field. i.e.

dU = -dW = – τ dθ

⇒ dU = – (- pE sinθ) dθ

⇒ dU =  pE sinθ dθ

Let the potential energy charges from U₁ to U₂ for the position of the dipole θ₁ and θ₂ respectively, then

\(\int_{U_1}^{U_2} dU = \int_{\theta_1}^{\theta_2} pE sin \theta d\theta\)

\(\Rightarrow U_2-U_1 = -pE(cos\theta_2 - cos\theta_1)\)

Now let θ = 90^o be taken as the reference position or zero potential energy, then

For θ₁ = 90^o; U₁ = 0

If θ₂ = θ, and  U₂ = U

⇒ U₂ – 0 = – pE (cos θ₂ – cos 90)

⇒ U  = – pE cosθ

Hence, the potential energy associated with an electric dipole is given by

U  = – pE cosθ

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Oscillation of Electric Dipole in Uniform Electric Field

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Consider an electric dipole placed in an equilibrium position in a uniform electric field such that the angle between the electric dipole moment vector p and the electric field is 0 i.e. θ = 0^o. Now when the dipole is displaced from its equilibrium position to an angle θ, then the restoring torque experienced by the dipole is

τ = -pE sinθ

Here negative sign indicates that the restoring torque tries to restore the dipole to its mean position.

For very small very of θ, sinθ ≈ θ, therefore

τ = -pEθ

Let the dipole possesses a moment of inertia I about the center of the dipole, then

τ = Iα

Where α is the angular acceleration of the dipole.

Combining the above two equations, we get

Iα = -pEθ

⇒ α = -(pE/I)θ

Comparing the above equation with the equation of angular acceleration in Simple harmonic motion, i.e.

α = -ω²θ

We get, ω² = pE/I

\(\Rightarrow \omega = \sqrt {\frac {pE}{I}}\)

But, ω = 2π/T (T is the time period of oscillation of the dipole)

\(\Rightarrow \frac {2\pi} {T} = \sqrt {\frac {pE}{I}}\)

Therefore, the equation of the time period of oscillation of the dipole is

\( T = 2\pi \sqrt {\frac {I}{pE}}\)

Also, T = 1/f (Where f is the frequency of the oscillation)

Therefore, the frequency of the oscillation of the dipole is

\( f =\frac {1}{T}= \frac {1}{2\pi} \sqrt {\frac {pE}{I}}\)

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Electric Potential Due to an Electric Dipole

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The electric potential at a point due to an electric dipole is the algebraic sum of electric potential due to the individual charges of the dipole at that point.

Consider an electric dipole of charges +q and -q separated by a certain distance. The electric potential at distance r from the center of the dipole is given by

\(V=\frac {pcos\theta}{4\pi \epsilon_o r^2}\)

Where

• p = dipole moment
• r = distance at which potential due dipole is to be calculated
• θ = angle between the position vector of the point at which the potential due dipole is to be calculated and the dipole moment

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Significance of Electric Dipole

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Electric Dipole deals with the study of the phenomenon and behavior of the opposite charges present around us and how they react if they are kept at a distance.

• In most molecules, the centers of positive and negative charges lie in the same place. Therefore, their dipole moment is zero. CO₂ and CH₄ are examples of this type of molecule. However, they develop a dipole moment when an electric field is applied.
• In Polar molecules, there are chances where the centers of negative and positive charges do not coincide. Therefore, they have a permanent electric dipole moment, even in the absence of an electric field. Water molecules, H₂O, are an example of this type of molecule.
• Various materials give rise to interesting properties and important applications in the presence or absence of electric fields.

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What is Coulomb’s law?

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Coulomb’s law basically refers to the quantitative statement about the force between the two point charges.

• Sometimes, the linear size of the charged bodies is much smaller than the distance separating them and in that case, the size may be ignored but the charged bodies are treated as point charges.
• Coulomb measured the force between two point charges and found that it varied inversely as the square of the distance between the charges and was directly proportional to the product of the magnitude of the two charges (positive and negative charge) and acted along the line joining the two charges.
• Thus, if two point charges q₁ and q₂ are separated by a distance (denoted as) r in a vacuum, the magnitude of the force (F) between them is given by:

F = \(k {q_1q_2 \over r^2}\)

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Previous Year Questions

1. If a charged spherical conductor of radius 10 cm has potential V at a point distant….
2. The value of A such that the electric field in the region between the spheres will be constant, is….[JEE Main 2016]
3. Let a total charge 2Q be distributed in a sphere of radius R….[JEE 2019]
4. If wires have mass λ per unit length then, the value is…. [JEE Main 2015]
5. A hollow metal sphere of radius RR is uniformly charged. The electric field due to the sphere... [NEET 2019]
6. In Millikan's oil drop experiment, the charge on an oil drop is….[VITEEE 2011]
7. What is the relation between q  and Q  if the two parts, when placed apart, have maximum coulomb repulsion…
8. A plane square sheet of charge of side 0.5m  has a uniform surface charge ….. [KEAM]
9. The maximum torque exerted by the field on the dipole is….
10. If the electric dipole is slightly rotated from its equilibrium orientation, then its angular frequency ω is…. [JEE Main 2019]

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Things to Remember

• An electric dipole is a pair of equal and opposite charges q and –q separated by a distance denoted as d.
• The formula for electric dipole moment is p = Qd.
• Molecules mostly have their positive and negative charges lying at the same place and therefore, their dipole moment is zero.
• The line along the direction of an electric dipole is called the axis of the dipole.
• The midpoint of locations of –q and q is called the center of the dipole.