An electric dipole is a system consisting of two equal and opposite charges separated by a small distance.
Electric dipoles are important in electrostatics because they help explain the behavior of molecules, electric fields, and dielectric materials.
Many molecules such as water behave like electric dipoles.
What is an Electric Dipole?
An electric dipole consists of:
- A positive charge +q
- A negative charge −q
- A small separation distance between them
If the distance between the charges is 2a, the arrangement forms an electric dipole.
The line joining the two charges is called the dipole axis.
Dipole Length
The distance between the positive and negative charges is known as the dipole length.
If each charge is at a distance a from the center, then:
Electric Dipole Moment
The strength of an electric dipole is measured by its electric dipole moment.
Electric dipole moment is defined as the product of either charge and the separation distance between the charges.
Mathematically,
Or simply,
Where:
- p = electric dipole moment
- q = magnitude of either charge
- d = separation between charges
- n̂ = unit vector from negative charge to positive charge
Direction of Dipole Moment
The direction of electric dipole moment is from the negative charge toward the positive charge.
This convention is universally used in electrostatics.
SI Unit of Dipole Moment
From the definition:
The SI unit is:
That is, coulomb-meter.
Electric Field Due to a Dipole
The electric field produced by a dipole depends on the position of the observation point.
Two important cases are studied:
- Axial position
- Equatorial position
Electric Field on the Axial Line
The axial line is the line passing through both charges.
For a point located at distance r from the center of the dipole, where r is much greater than a:
The electric field is directed along the dipole axis.
Electric Field on the Equatorial Line
The equatorial line is the perpendicular bisector of the dipole.
For a point at distance r from the center:
The direction of the electric field is opposite to the dipole moment.
Comparison of Axial and Equatorial Fields
From the formulas:
Thus, the electric field on the axial line is twice that on the equatorial line at the same distance.
Electric Potential Due to a Dipole
The electric potential at a point due to a dipole is:
Where:
- p = dipole moment
- r = distance from the dipole center
- θ = angle between dipole axis and position vector
Potential on the Axial Line
For θ = 0°:
Potential on the Equatorial Line
For θ = 90°:
Therefore,
The electric potential on the equatorial line of a dipole is zero.
Dipole in a Uniform Electric Field
When an electric dipole is placed in a uniform electric field, equal and opposite forces act on the charges.
The net force is zero.
However, a torque acts on the dipole.
Torque on an Electric Dipole
The torque experienced by a dipole in a uniform electric field is:
Where:
- τ = torque
- p = dipole moment
- E = electric field intensity
- θ = angle between p and E
The torque tends to align the dipole along the electric field.
Potential Energy of a Dipole
The potential energy of a dipole in a uniform electric field is:
Important cases:
Stable Equilibrium
Potential energy is minimum.
Unstable Equilibrium
Potential energy is maximum.
Applications of Electric Dipoles
- Study of polar molecules
- Dielectric materials
- Capacitor theory
- Molecular bonding analysis
- Electrostatic field calculations
Solved Example
An electric dipole consists of charges ±2 μC separated by 4 cm.
Find the dipole moment.
Given:
Using:
Substituting values:
Therefore,
Important Points to Remember
- An electric dipole consists of equal and opposite charges.
- Dipole moment is given by p = qd.
- Its direction is from negative charge to positive charge.
- SI unit of dipole moment is C·m.
- Axial field is twice the equatorial field.
- Potential on the equatorial line is zero.
- A dipole experiences torque in a uniform electric field.
- Potential energy is U = −pE cosθ.
Frequently Asked Questions
What is an electric dipole?
An electric dipole consists of two equal and opposite charges separated by a small distance.
What is electric dipole moment?
It is the product of charge and separation distance.
What is the SI unit of dipole moment?
What is the potential on the equatorial line of a dipole?
What torque acts on a dipole in a uniform electric field?
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