All the complexity of the universe around us ultimately comes from four fundamental forces: gravity, the strong nuclear force, the weak nuclear force and electromagnetism. Electromagnetism can be a challenging topic to study, but the basics of what the force is and how it works are fairly straightforward, and the Lorentz force law, in particular, tells you the key points you need to understand. In a nutshell, the electromagnetic force causes unlike charges – positive and negative – to attract one another, and unlike charges to repel.

#### TL;DR (Too Long; Didn't Read)

Electromagnetism is one of the four fundamental forces in the universe. It describes how charged particles react to electric and magnetic fields, as well as the fundamental links between them. Electromagnetic force, like all forces, is measured in Newtons.

Electrostatic forces are described by Coulomb’s law, and both electric and magnetic forces are covered by the Lorentz force law. However, Maxwell’s four equations provide the most detailed description of electromagnetism.

## Electromagnetism: The Basics

The term electromagnetism combines the electric and magnetic forces into a single word because both forces are due to the same underlying phenomenon. “Charged” particles generate electric fields, and positive and negative charges react to that field differently, which explains the force we observe. For electric interactions, positively charged particles (like protons) push away positively charged particles and attract negatively charged ones (like electrons), and vice versa. Electric field lines spread directly outward from positive electric charges, and this pushes particles in the direction of – or in the opposite direction to – the field lines.

Magnetism comes from magnetic fields, which are generated by moving charges. Particles don’t respond to magnetic fields in the same way as they do to electric fields. Magnetic field lines form circles, with no beginning or end. In response to them, particles move in a direction perpendicular to both their motion and the field line. As with electric forces, positively charged particles and negatively charged ones move in opposite directions.

The electromagnetic force is the second strongest force in nature. The strong nuclear force is the strongest, electromagnetic forces are 137 times less powerful, the weak nuclear force is a million times smaller, and gravity is much, much smaller than the rest (about 6 × 10^{−}^{39} times weaker than the strong nuclear force).

## Electrostatic Forces and Coulomb’s Law

“Electrostatic force” refers to the electric force generated by stationary charges. It is described by a simple equation known as Coulomb’s law. This states that:

* F* =

*kq*

_{1}

*q*

_{2}/

*r*

^{2}

Here, *F* means force, *k* is a constant, *q*_{1} and *q*_{2} are the charges, and *r* is the distance between them. Bigger charges produce a bigger force, and more separation weakens the strength of the force. As with all forces, electromagnetic force is measured in Newtons (N). The constant *k* has a specific value, 9 × 10^{9} N m^{2} / C^{2}. Charge is measured in coulombs (C), and you input the sign of the charge (+ or −) along with the strength, so the equation has a positive value for repulsion and a negative one for attraction.

## The Lorentz Force Law

The Lorentz force law incorporates both magnetic and electric forces, so it is one of the best representations of the electromagnetic force. The law states:

*F** *= *q* (** E** +

*v*

**×****)**

*B*Where ** E** is the magnetic field,

**is the velocity of the particle, and**

*v***is the magnetic field. These are bolded because they are vectors, which have a direction as well as a strength, and the**

*B***symbol is bolded because this is a vector product rather than a simple multiplication. The equation tells us that the total force is the sum of the electric field and the vector product of the velocity of the particle and the magnetic field, all multiplied by the charge of the particle. The vector product produces a force in a direction perpendicular to both, in line with the previous section.**

**×**## Electromagnetism in Action: Atoms, Light, Electricity and More

Electromagnetism shows itself in many forms in day-to-day life and physics. Atoms are held together by the electromagnetic attraction between the protons in the nucleus and the electrons orbiting it. Light is an electromagnetic wave, where an oscillating electric field generates a changing magnetic field, which in turn creates an electric field, and so on. This is predicted by Maxwell’s equations (four equations which explain everything about electromagnetism in the language of vector calculus), including the characteristic speed at which it travels.

Electromagnetism is also responsible for the electricity powering your screen and the device you’re reading on, with the flow of electrons propelled along electric field lines providing the energy. These examples only scratch the surface of the wide range of phenomena explained by electromagnetism.