22.16:
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.
22.16:
Induced Electric Dipoles
A permanent electric dipole orients itself along an external electric field. This rotation can be quantified by defining the potential energy because the external torque does work in rotating it. Then, the potential energy is minimum at the parallel configuration and maximum at the antiparallel configuration. While the former is a stable equilibrium, the latter is an unstable equilibrium.
Since the absolute value of potential energy holds no physical meaning, its zero value can be chosen as per convenience. It is chosen to be in the configuration when the electric dipole is perpendicular to the field.
The polarity of molecules determines whether they are a good solvent. For example, water is a good solvent for common salt because it attracts the positive and negative ions toward the opposite charge centers inside it, thereby breaking apart the sodium chloride crystals.
Not all molecules, however, possess a permanent electric dipole. If the positive and negative charge centers are located at the same point, there is no separation. For example, the molecular structure of carbon dioxide is symmetric in the charge distribution. Other organic compounds, such as methane, are also non-polar.
However, in the presence of an external electric field, the charge centers are separated because the negative charge center shifts toward the electric field, while the positive charge center shifts away from the field. Since this happens for all molecules, the external field induces a polarity across the substance.
It is interesting to note that the induced dipole moment somewhat nullifies the electric field. This scenario arises near the dipole, where its electric field is opposite to the external electric field. This mechanism reduces the electric field inside dielectrics.
Suggested Reading
- Young, H.D and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson; section 21.7; page 711.
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from 5.7 Electric Dipoles – University Physics Volume 2 | OpenStax; page 218.