Electric Dipole
An electric dipole is a pair of positive and negative charges with equal magnitude and separated by a small distance. For example, two opposite charges +q and -q having a distance d between them is a dipole.
Example of an electric dipole is hydrogen fluoride (HF) gas. HF is a covalent compound. Hydrogen and Fluorine both share their electrons. But fluorine has a greater tendency of attracting electrons than hydrogen, so fluorine pulls the shared electrons towards it and HF becomes a polar molecule. The Fluorine molecule becomes negatively charged and the Hydrogen molecule becomes positively charged. Thus, HF becomes a dipole.
Electric Dipole Moment
Let we put a dipole inside an uniform electric field E.
If a charge of q is put in an electric field E, then the electric force on the charge is,
F = E * q
For a positive charge, the direction of F is the same as the direction of E. For a negative charge the direction of the force is opposite to the direction of the electric field. So, the +q and the -q charges of the dipole will feel forces with the same magnitude but opposite in directions.
These two forces acting on +q and -q charges are parallel but opposite in direction. Both of the forces have same magnitude. If two parallel forces with same magnitude and opposite directions works on a body, it creates a torque. This torque causes the rotation of the body. The magnitude of the torque is the magnitude of force times the distance between the parallel forces.
For the dipole, two parallel forces are acting on the dipole in opposite directions and both of the forces have same magnitude. So, the torque acting on the dipole is the electric force F times distance between the two forces.
The distance between the two forces is not d, as d is not the perpendicular distance between the parallel lines (green dotted lines). The distance between the two forces is r. So, the torque on the dipole
τ = r * F
If we consider the angle between d and E be Ө, then
r = d * sin Ө
So, the torque is,
The force F = E*q
As the rotation of the dipole is clockwise, according to the right hand rule the direction of τ is perpendicular to the page and points into the page.
According to the right hand rule of cross product, the direction of d must be from negative charge to positive charge. Otherwise, the direction of cross product (d x E) will not be the same as the direction of τ. If the direction of d is considered as from negative charge to positive charge then the cross product (d x E) will have the same direction as τ. So, the direction of d is from negative charge to positive charge.
The product of q and d is defined as the dipole moment p.
As d is a vector quantity, so p is also a vector. The direction of p is the same as the direction of d, from negative charge to positive charge. So, the torque on the dipole can be written as,
