Electricity and magnetism might seem like two separate forces based on your everyday life. Most of the time, when you talk about electricity, you’ll be referring to electric current or electric charges that power household appliances from your laptop to something as simple as a light bulb.

Magnetism isn’t as commonly encountered, but every school kid will have come into contact with bar magnets before, which have a north pole and a south pole, with like poles repelling and opposite poles attracting.

## Electricity and Magnetism in Physics

This everyday understanding of electric charges and the magnetic force will give you a pretty good basic understanding of how electricity and magnetism work, but there is much more to learn, from the origin of magnetic poles to Ohm’s law, electromagnetic induction and beyond.

While your day-to-day experience of electricity and magnetism can get you through everyday situations, if you’re taking physics at higher levels, you need a much deeper understanding of the phenomena.

Thanks to the work of pioneering physicists like Michael Faraday and James Clerk Maxwell, scientists now understand that electricity and magnetism aren’t separate forces at all, but different aspects of the one of the four fundamental forces: **electromagnetism.**

The key realization behind this was that magnetic fields are actually produced by moving electric charges. The electromagnetic force is completely described by **Maxwell’s equations**, and by the end of this article you’ll understand what each one is and what it tells you.

## What Is Electricity?

Electricity is the colloquial name for the effect of the electric force, which in most cases involves the interaction between protons (the positively-charged particles in the nucleus of every atom) and electrons (the negatively-charged particles that exist in a cloud around the nucleus).

When a charged particle is close to another charged particle – for example two electrons near each other or an electron and a proton near each other – they have an interaction which can generally be described using Coulomb’s law. Broadly speaking, though, like charges repel and opposite charges attract – just like matching and opposite poles on a magnet.

**Coulomb’s law** states that for two charges, *q*_{1} and *q*_{2}, separated by a distance *r*, the electric force has the magnitude:

F = \frac{kq_1q_2}{r^2}

Here, *k* = 1 / 4πε_{0} = 9 × 10^{9} N m^{2} / C^{2} and ε_{0} is a constant called the permittivity of free space. If you’re familiar with the law of universal gravitation, you’ll notice that Coulomb’s law has a very similar form, with the charges in place of the masses and *k* in place of *G*. In particular, both are inverse square laws, so moving the charge twice as far away decreases the strength of the force by a factor of four.

However, you can also describe the electric force using the concept of an electric field, which is defined as the strength of the force on a “test charge,” and is defined throughout space with a value in Newtons per Coulomb.

The electric field is a **vector**, though, so it has both a strength *and* a direction. While you can define the electric field strength *E* simply as *E* = *F* / *q*, where *q* is the test charge, the most useful equation for this is Gauss’ law, one of Maxwell’s equations, which will be covered later.

## What Is Magnetism?

Magnetism is a little bit more complicated than electricity to describe in a mathematical way, but the basic principles are very similar. Just as electric forces are described as occurring between positive charges and negative charges, so magnetic forces are described as occurring between north poles and south poles (or positive and negative poles) of magnets.

In exactly the same way as for electric forces, like poles repel, and opposite poles attract. Magnetic forces can also be described using the concept of magnetic fields, which – like electric fields – are invisible fields that permeate space and represent the ability of the magnetic force to change the velocity of charged particles in the vicinity.

However, magnetic poles only exist in pairs, as dipoles – **there are no magnetic monopoles**. If magnetic monopoles did exist, there would be a simple law like Coulomb’s law that applied to magnetism rather than electricity, but magnetism is inherently a little more complicated than this, and so magnetic forces tend to be described based on the magnetic fields generated by specific sources. For example, there is an equation for the magnetic field of a solenoid, the field produced by a wire carrying an electric current and so on.

Magnetic fields are generally measured in units of either Teslas (T) – named after physicist Nikola Tesla – or gauss (G) – named after Carl Friedrich Gauss – and 1 T = 10,000 G. This is technically a measure of magnetic flux density, but to avoid getting bogged down in the precise details it’s safe to just think of this as meaning roughly the same thing.

A strong magnet in a lab will have a value of about 1 T, while a refrigerator magnet will be more like 0.1 T, so Gauss is often the better unit to use for everyday magnetic fields.

## The Lorentz Force Law and Magnetism

If you don’t want to work with Maxwell’s equations, which are generally much more complicated, the best way to calculate the force of magnetism is using the **Lorentz force law**. This is a law that encompasses both magnetic and electric fields, combining two different terms to predict the force imparted on a particle under the influence of both and the direction of the resulting force.

For the magnetic force, the relevant part of the Lorentz force law is:

\bold{F} = q\bold{v × B}

Where *q* is the charge of the particle traveling through the field, **v** is its (vector) velocity, and **B** is the magnetic field. You should also note that the **×** symbol is not a simple multiplication, but instead a **vector product**, which produces a force in a direction given by the right hand rule. Simply, the strength of the force imparted on the particle is given by:

F = qvB \sin (θ)

Where the angle *θ* is the angle between the direction of the velocity of the particle and the magnetic field. This immediately tells you that the interaction is strongest when the particle is traveling at a 90 degree angle (i.e. perpendicular) to the magnetic field.

## The Lorentz Force Law

The Lorentz force law’s full form allows you to account for the electric field as well as the magnetic field and has the form:

\bold{F} = q(\bold{E+v × B})

Where again the *q* is the charge of the particle, **v** is its velocity, and **B** is the magnetic field strength, but now the contribution of the electric field **E** has been taken into account. If you have the value of the magnetic field, the electric field, the charge of the particle and its velocity, you can calculate the force and its direction relatively easily using the Lorentz force law.

The only problem is that if you *don’t* know the details about the magnetic field, you’ll still need to use Maxwell’s equations to derive them.

## Electromagnetism and Applications

Electromagnetism has a huge range of useful applications, in particular related to household electricity and the generation of power.

For a simple example, the fact that moving charges produce an electric field can be used to create an electromagnet: a coil of wire with current flowing through it will produce a basic electromagnet. Huge, high-power versions of this same basic technology is used to move cars and scrap metal in junkyards, and this is much more useful than a permanent magnet for this purpose because it can be turned off to drop the metal.

Electromagnetic induction is another aspect of electromagnetism with many applications. This is a characteristic quality of the fundamental link between electricity and magnetism: Just as a moving charge generates a magnetic field, a changing magnetic field can be used to induce a current in a wire.

This can be done by simply moving a magnet backward and forward in the middle of a coil of wire, or you can use alternating current (AC) electricity to generate a continuously varying magnetic field, and use this to induce a current in a wire.

These simple techniques underlie the operation of crucial tools like power generators and electric motors. Power generators work by moving a conductive wire in a magnetic field, thus inducing an electric current.

Electric motors, on the other hand, use a loop of current-carrying wire inside a magnetic field: When current flows in the wire, it generates a magnetic field, interacting with the existing magnetic field and causing the wire to move in the process. In short, generators turn motion into current, and motors turn current into motion.

## Maxwell’s Equations

The whole subject of electromagnetism is best described by Maxwell’s equations. There are four equations in total: Gauss’ law, the no monopole law, Faraday’s law and Ampere’s law. These are written in the language of vector calculus, and are as follows:

**Gauss’ law:**

\int \bm{E} ∙ d\bm{A} = \frac{q}{ε_0}

Where *E* is the electric field, *q* is the total charge, and *ε*_{0} is the permittivity of free space. In words, this says that the electric flux out of any closed surface is equal to the enclosed charge divided by the permittivity of free space.

**No monopole law:**

\int \bm{B} ∙ d\bm{A} = 0

Which states that the magnetic flux out of any closed surface is zero – in other words, magnetic monopoles don’t exist!

**Faraday’s law:**

\int \bm{E} ∙ d\bm{S} = − \frac{∂ϕ_B}{∂t}

Where *ϕ*_{B} is the magnetic flux. This states that the electric field around a closed loop is equal to minus the rate of change of the magnetic flux through that loop – this law describes the process of inducing a current in a wire using a changing magnetic field.

**Ampere’s law:**

\int \bm{B} ∙ d\bm{S} = − = μ_0I + \frac{1}{c^2}\frac{∂}{∂t}\int \bm{E} ∙ d\bm{A}

Where *μ*_{0} is the permeability of free space, and *I* is the current flowing through the loop. This states that the line integral of the magnetic field around a closed loop is proportional to the current flowing through the same loop – in other words, that electric currents generate magnetic fields.

## Using Maxwell’s Equations

While the mathematical language of Maxwell’s equations is complex (and couldn’t be introduced sufficiently in this article), you should already understand the principles of electromagnetism they convey.

The process of using the equations usually involves choosing an appropriate equation – Gauss’ law for calculating an electric field due to some collection of charge, Faraday’s law for calculating the induced electric field due to a changing magnetic field, and Ampere’s law for calculating magnetic fields caused by an electric current – and then performing an integral over an appropriately-chosen surface or an area to solve. The surface or flat area is purely theoretical, but it’s used to characterize the fields in three-dimensional space.

This can often be simplified if you assume a uniform field through your chosen surface or area. For example, Gauss’ law for a sphere of enclosed charge can simply be written:

E 4πr^2 = \frac{q}{ε_0}

Which you can see simplifies its use considerably. It also makes it clear that you can *derive* Coulomb’s law from this equation.