1. Concept Overview
An electric dipole is one of the most important charge arrangements in electrostatics. It consists of two equal and opposite charges separated by a small distance. Even though the total charge of a dipole is zero, it produces interesting electric fields and behaves strongly in external electric fields. Dipoles appear in molecules, insulators and many practical systems.
2. Definition of an Electric Dipole
An electric dipole is a system of two equal and opposite point charges (+q and -q) separated by a fixed distance 2a.
The centre of the dipole lies midway between the two charges.
3. Dipole Moment
The most important quantity associated with a dipole is its dipole moment.
3.1. Definition
Dipole moment is a vector quantity defined as:
\( \vec{p} = q \cdot 2a \; \hat{d} \)
It points from the negative charge to the positive charge.
3.2. Magnitude
\( p = q(2a) \)
Bigger charge or larger separation gives a stronger dipole.
3.3. Units
The SI unit of dipole moment is C·m (coulomb-metre).
4. Types of Dipoles
Dipoles appear in many forms in nature and practical systems.
4.1. Permanent Dipole
Some molecules, like water (H₂O), naturally have a positive and negative side due to their structure.
4.2. Induced Dipole
Sometimes a neutral object becomes a dipole when placed in an external electric field. Charges shift slightly, creating temporary positive and negative regions.
5. Electric Field of a Dipole (Qualitative Idea)
A dipole creates a unique electric field pattern. The field is strong near the charges but decreases rapidly with distance. Unlike a single charge, a dipole's field falls as \( 1/r^3 \) for large distances.
5.1. Direction of Field
- Along the axis: points away from +q and toward -q.
- On the perpendicular bisector: points from positive to negative side.
6. Behaviour of a Dipole in an External Electric Field
Even though the net charge of a dipole is zero, it still reacts strongly to external fields.
6.1. Force on a Dipole
In a uniform electric field, the net force on the dipole is zero because forces on +q and -q cancel each other.
6.2. Torque on a Dipole
The dipole experiences a turning effect (torque) that tries to align it with the electric field.
\( \tau = pE \sin \theta \)
Here, \( \theta \) is the angle between the dipole moment and the field.
6.3. Equilibrium Positions
- Stable equilibrium: dipole moment aligned with the field.
- Unstable equilibrium: dipole moment opposite to the field.
7. Potential Energy of a Dipole in an Electric Field
The energy stored in a dipole placed in a uniform electric field depends on its orientation.
7.1. Formula
\( U = -pE \cos \theta \)
The dipole has minimum energy when aligned with the field and maximum energy when opposite.
8. Worked Examples
8.1. Example 1: Finding Dipole Moment
A dipole has charges \( +4 \times 10^{-6} \text{ C} \) and \( -4 \times 10^{-6} \text{ C} \) separated by \( 0.02 \text{ m} \). Dipole moment:
\( p = q(2a) = 4 \times 10^{-6} \times 0.02 = 8 \times 10^{-8} \text{ C·m} \).
8.2. Example 2: Torque on a Dipole
A dipole with \( p = 3 \times 10^{-8} \text{ C·m} \) is placed in a field \( E = 2000 \text{ N/C} \) at \( 30^\circ \). Torque:
\( \tau = pE \sin \theta = 3 \times 10^{-8} \times 2000 \times 0.5 = 3 \times 10^{-5} \text{ N·m} \).
9. Physical Interpretation
An electric dipole behaves like a tiny compass needle in an electric field. Just as a magnetic needle aligns with a magnetic field, a dipole rotates to align with an electric field. The idea of a dipole helps describe many natural systems, especially molecules that have separated positive and negative regions.