An electric dipole is a system of two equal but opposite charges, separated by a fixed distance. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, but only under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is equivalent to heat at the molecular level.
Consider a...

The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...

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...

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...

Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.Polar molecules have a partial positive charge on one end and a partial negative charge on the other end of the molecule,...

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...