Induced Electric Dipoles

When a permanent dipole, like a water molecule, is placed in an external electric field, the torque orients it along the field.

Its potential energy change is given by the negative work done to rotate it, which is an integral of the torque and differential angle's dot product. By choosing the potential energy to be zero at the perpendicular orientation, the potential energy at any angle is obtained. It is the negative dot product of its dipole moment and the field, which can be plotted.

Not all molecules are permanent dipoles. In a carbon dioxide molecule, the negative charge center coincides with the positive charge center, resulting in zero dipole moment.

In the presence of an external electric field, the positive charge is repelled away from the field while the negative charge is pulled toward it, resulting in a net dipole moment.

The charge separation induces an electric field. In its vicinity, it is opposite to the external field, while at large distances, it reinforces it.

The net electric field is the vector sum of the two fields.