What is Electric Dipole? Definition, Formula & Class 12 Notes

When two equally opposite charges are separated by a small distance, this system of charges is known as an Electric dipole.

A big question is, since both charges are opposite in nature, why don't they fall into each other? 

In reality, the electric dipole doesn't exist as a free system of charges; there is always an external force, such as inter ot intramolecular forces, or external mechanical forces, which balances both charges. 

There are three important constituents of an electric dipole.

1. A positive charge is denoted by $+q$
2. Negative charge is denoted by $-q$
3. Distance between charges $2a$

Key properties of Electric Dipole

It inhibits some special properties. It is important to know the properties asked in the board exams. Read the properties below;

• The electric field at the midpoint joining the line is always zero.
• An electric dipole produces an electric field even the its net charge as a system is zero.
• The dipole moment represents the directionality and possible force exerted on the dipole when placed in a field. 
• The electric field due to a dipole decreases with distance.

An electric dipole is a very important concept in class 11 physics. You can check the class 11 dipole moment and related properties below.

Dipole Moment

The dipole moment of an electric dipole provides a measure of polarity, which means it shows strength and direction. Since it is a vector quantity, it indicates the direction of polarity. It is calculated as the product of the magnitude of the charge and the distance between these two charges (separation distance). 

So, mathematically,

$\vec{p}=q\cdot 2\vec{a}$

where:

$\vec{p}$ = dipole moment

$q$ = magnitude of each charge

$2a$ = distance between charges

Direction of Dipole Moment

We fixed the direction of the dipole moment according to a convention agreed upon (by the scientific world). The scientific community has fixed the direction which negative charge to positive charge for convenience. 

If you draw a line from the negative charge towards the positive charge, colinear to the axis of the dipole, this will represent the direction of the dipole moment.

Let's assume there is an electric dipole with two charges: +q and -q. These charges are separated by a distance d. if we divide this distance d in a way that the O is mid midpoint and the distance of the charge from mid midpoint is r. 

Then the formula for electric potential;

The electric potential due to a dipole: $\begin{array}{l}V=\frac{1}{4\pi ϵ}\frac{pcos\theta }{r^2}\end{array}$

In case, θ = 90°

Electric Potential (V) = 0

When, θ = 0°

$\begin{array}{l}\text{Electric potential}=V=\frac{1}{4\pi ϵ}\frac{p}{r^2}\end{array}$

You can solve these practice questions below for better understanding.

1. A dipole with two charges of equal and opposite charges with magnitude $q=2\mu \mathrm{C}$ separated by a distance $2a=0.01\mathrm{m}$ in a uniform field $E=1000{\mathrm{N}\mathrm{C}}^{-1}$ . The angle between E and the axis of the dipole $\theta ={60}^{\circ }$ . Find the torque.

$\begin{array}{c}p=q\cdot 2a=2\times {10}^{-6}\times 0.01=2\times {10}^{-5}\mathrm{C}\mathrm{m}\\ \tau =pE\mathrm{s}\mathrm{i}\mathrm{n}{60}^{\circ }=\left(2\times {10}^{-5}\right)\times 1000\times \frac{\sqrt[]{3}}{2}\approx 0.0173\mathrm{N}\mathrm{m}.\end{array}$

2. What will be the electric field at a point 0.1 m away from a dipole that has a dipole moment $p=1\times {10}^{-6}\mathrm{C}\mathrm{m}$ on its axial line?

$E=\frac{1}{4\pi {ϵ}_0}\frac{2p}{r^3}=9\times {10}^9{\mathrm{N}\mathrm{m}}^2{\mathrm{C}}^{-2}\times \frac{2\times {10}^{-6}}{(0.1{)}^3}=1800{\mathrm{N}\mathrm{C}}^{-1}.$