(a) Electric dipole. A system of two equal and opposite charges separated by certain distance is called electric dipole.
Fig. shows an electric dipole consisting of two equal and opposite point charges (± q) separated by a small distance 2a.
Dipole moment (\(\vec P\)). It is defined as the product of magnitude of either charge and the distance between two charges.
i.e. \(\vec P= q\vec {2a}\)
The direction of \(\vec p\) is from -ve charge to +ve charge.
Units: In S.I.,
The unit of \(\vec p\) is Coulomb-metre (Cm).
Dipole field. The electric field produced by an electric dipole is called electric dipole field and is defined as the space around an electric dipole within which the effect of the dipole can be felt.
Electric lines of force. Below Fig. shows the section of the field in the plane of paper, containing dipole itself.
The lines of force are directed away from +q charge and towards -q charge. They are straight and open along the line containing the charges. This line is called axial line of dipole. On the broad side of the dipole, lines are curved. Near the dipole, they start from +q charge and end at -q charge, then closing their path at the ends of the dipole.
(b) Intensity of dipole field
Let an electric dipole have charge strength q and length a. So its dipole moment p = qa. Let it lie along z-axis with its centre at origin O, charges q at position z = a/2 and charges -q at position z = - a/2.
Let the poles have the position vectors \(\vec r_1\) and \(\vec r_2\) as shown in Fig. ahead. So \(\vec r_1\) has co-ordinates (0, 0, a/2) and \(\vec r_2\) has co-ordinates (0, 0, -a/2).
This expression holds true when r > > a.
In case of point dipole, a → 0, we write qa = p
Then \(\vec E(\vec r)= \frac{p}{\piɛ_o} \frac{1}{r^3}[3xz\hat i\ +\ 3yz\hat j\ +\ (3z^2\ -\ r^2)\ \hat k]\)
This is the expression for intensity of electric field of an ideal point dipole at all points in the space. The field has cylindrical symmetry with the axis of dipole as axis of the cylinder.
