Physical Significance of Dipoles

Why Dipoles Matter: Polar vs. Non-Polar Molecules

Most molecules have their positive and negative charge centres at the same point, so their net dipole moment is zero. Examples include $\text{CO}_2$ and $\text{CH}_4$. Such molecules can develop a temporary dipole moment only when an external electric field is applied.

However, in some molecules — called polar molecules — the centres of positive and negative charge do not coincide. These possess a permanent electric dipole moment even without any external field. A classic example is the water molecule, $\text{H}_2\text{O}$. The presence or absence of a permanent dipole gives materials very different electrical properties and leads to many important applications.

Electric Field of a Dipole: The Far-Field Approximation

When we are far away from a dipole (distance $r$ from the centre is much larger than the separation $2a$ between the charges, i.e., $r \gg a$), the electric field can be expressed using simple formulas. These formulas are derived from the exact calculation, as shown in the textbook example.

1. Field on the Axis (End-on Position)

For a point on the axis of the dipole, at a distance $r$ from the centre, the magnitude of the electric field is:

• $p$ is the magnitude of the dipole moment: $p = q \times (2a)$, where $q$ is the charge magnitude and $2a$ is the separation.
• $\varepsilon_0$ is the permittivity of free space ($8.854 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2}$).
• $r$ is the distance from the centre of the dipole to the point.
• Direction: The field is along the direction of the dipole moment vector (from the negative charge to the positive charge).

2. Field on the Equatorial Line (Perpendicular Bisector) …