Electric Dipole
An electric dipole consists of two equal and opposite electric charges (+q and −q) separated by a small distance (2a or d), characterised by the electric dipole moment — a vector quantity pointing from the negative to the positive charge. The dipole model is fundamental to understanding molecular polarity, dielectric materials, antenna radiation patterns, and the interaction of matter with electric fields. The electric field pattern of a dipole is more complex than that of a point charge, with field strength varying as 1/r³ at large distances.
Key Formula
p = q × d
LaTeX: \vec{p} = q \cdot \vec{d}
| Symbol | Meaning | Unit |
|---|---|---|
| p | Electric dipole moment (vector, points from −q to +q) | Coulomb·metre (C·m) |
| q | Magnitude of each charge | Coulomb (C) |
| d | Separation distance between the two charges | Metre (m) |
Worked Example
Problem
Two charges +3 nC and −3 nC are placed 4 cm apart. Calculate the electric dipole moment and state its direction.
Solution
Step 1: Identify the values. q = 3 nC = 3 × 10⁻⁹ C d = 4 cm = 4 × 10⁻² m Step 2: Calculate the dipole moment magnitude. p = q × d p = 3 × 10⁻⁹ × 4 × 10⁻² p = 12 × 10⁻¹¹ C·m p = 1.2 × 10⁻¹⁰ C·m = 0.12 nC·m Step 3: State the direction. The dipole moment vector p points from the negative charge (−3 nC) to the positive charge (+3 nC), by convention.
Answer
p = 1.2 × 10⁻¹⁰ C·m, directed from −3 nC towards +3 nC
Electric Field of a Dipole at Special Points
| Position | Distance from Centre | Electric Field Formula | Direction |
|---|---|---|---|
| On axial line (end-on) | r >> d | E = 2kp / r³ | Along dipole axis (same as p) |
| On equatorial line (broadside-on) | r >> d | E = kp / r³ | Antiparallel to p |
| General point | r | E = kp√(3cos²θ+1) / r³ | Depends on angle θ |
| At r → ∞ | Very large | E → 0 | Field vanishes at infinity |
| Midpoint between charges | 0 | E = kq/a² (towards −q) | Towards negative charge |
Interactive Tools
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Related Terms
Maxwell's Equations
Maxwell's Equations are a set of four partial differential equations formulated by James Clerk Maxwell (1861–1865) that completely describe the behaviour of electric and magnetic fields and their interactions with matter and charge. They unify electricity, magnetism, and optics into a single coherent theory and predicted the existence of electromagnetic waves travelling at the speed of light. Maxwell's Equations are among the greatest achievements in theoretical physics and form the foundation of classical electrodynamics, modern optical theory, and electrical engineering.
Electromagnetic Wave
An electromagnetic wave is a self-propagating transverse wave consisting of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation. Predicted theoretically by James Clerk Maxwell in 1865 and confirmed experimentally by Heinrich Hertz in 1887, electromagnetic waves require no medium and travel at the speed of light (3 × 10⁸ m/s) in vacuum. The electromagnetic spectrum spans radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays — all governed by the same wave equations.
Direct Current
Direct current (DC) is an electric current that flows consistently in one direction, with charge carriers (typically electrons) moving from the negative terminal to the positive terminal of a source. Unlike alternating current, the magnitude of DC does not periodically reverse; it may be steady or vary in magnitude but never changes polarity. DC is produced by batteries, fuel cells, solar cells, and rectifiers, and is essential in electronics, mobile devices, electric vehicles, and renewable energy storage systems.
"Dipole" from Greek "di" (two) and "polus" (pole or axis), meaning "two poles". The concept was formalised in the 19th century in electrostatics and extended to molecular chemistry in the 20th century. In antenna theory, the half-wave dipole antenna designed by Heinrich Hertz in 1886 takes its name from this same concept.