22.15:
Electric Dipoles and Dipole Moment
When two equal but opposite point charges are held together, the pair is called a dipole. If it does not separate due to external forces, it is called a permanent dipole.
In a water molecule, the centers of negative and positive charges are close but do not coincide, making it a permanent dipole.
In a uniform electric field, the charges experience forces that are equal but opposite, resulting in zero net force. However, the dipole experiences a net torque.
Choose any origin, and consider the position vectors of the charges. The torque on each component is obtained.
Upon vector addition, the net torque is given by the cross product of a new vector with the electric field. It is the product of the charges' magnitude and the displacement vector of the positive charge with respect to the negative charge. This is called the electric dipole moment.
The torque rotates the dipole along the field.
If it is anti-parallel, it experiences zero net torque but is in an unstable equilibrium, as slight deviations lead to a torque that rotates it parallel.
22.15:
Electric Dipoles and Dipole Moment
Consider two charges of equal magnitude but opposite signs. If they cannot be separated by an external electric field, the system is called a permanent dipole. For example, the water molecule is a dipole, making it a good solvent.
Theoretically, studying electric dipoles leads to understanding why the resultant electric forces around us are weak. Since electric forces are strong, remnant net charges are rare. Hence, the interaction between dipoles helps us understand electrical interactions in ordinary objects around us.
When a permanent dipole is placed in a uniform electric field, it experiences no net force. However, it orients itself along the field so that the positive charge end points toward it. This interaction between the dipole and the electric field can be scrutinized by calculating the net torque it experiences.
Simple vector algebra leads to an interesting observation. The net torque depends on a cross-product of a new vector, called the electric dipole moment, and the electric field. The dipole moment is proportional to the magnitude of each charge and the separation between them.
If a molecule has a large separation between its positive and negative charge centers, it has a higher dipole moment. If the charge separated is itself high, its dipole moment is larger.
The dipole moment points from the negative charge to the positive charge. In the absence of any other torque, the dipole rotates and aligns with the field. The observation implies that the potential energy is associated with the orientation of the dipole with respect to the external electric field.
Suggested Reading
- Young, H.D and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson; section 21.7; page 709.
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from 5.7 Electric Dipoles – University Physics Volume 2 | OpenStax; page 217.