Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the nucleus...

Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...

If a magnetic field is sustained, there must be a current in a closed circuit or loop, implying some energy has been spent in creating the field. If this energy is not dissipated via the circuit's resistance, it is stored in the field.
Take an ideal inductor with zero resistance. Although it's practically impossible, assume that the coil's resistance is so small that it is practically negligible. The loss of the field's energy to dissipate thermal energy (or heat) is thus negligible.
The energy...

Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun's warmth. At other times, it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells. Electromagnetic waves bring energy into a system through their electric and magnetic fields. These fields can exert forces and move charges in the system and, thus, do work on them. However, there is energy in an electromagnetic wave,...

The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.

The internal energy of a molecule is determined by its degrees of freedom, including translational, rotational, and vibrational motions. In addition to these kinetic activities, the energy of molecules is also shaped by electronic energy, intermolecular forces, and the rest-mass energy of electrons and nuclei. These factors collectively influence the energy state of the molecules. The equipartition theorem of classical mechanics provides insight into this energy distribution. It posits that the...