eolas/zk/Electromagnetism.md

---
tags: [physics, electricity, electromagnetism]
---

# Electromagnetism

> Electromagnetism is the physical interaction among **electric charges,
> magnetic moments and the electromagnetic field**.

For a long time electricity and magnetism were thought to be separate forces. In
the 19th century Maxwell demonstrated that they were interrelated phenomena then
Einstein proved with the Special Theory of Relativity that they are aspects of
one unified phenomenon.

The core of the relationship is that a changing magnetic field produces an
electric field and conversely, a changing electric field produces a magnetic
field.

## Electric charge

We know that charge is an innate property of all charged fundamental particles.
If a particle is charged it has a positive or negative charge. The most common
charged particles in the universe are negatively charged electrons or positively
charged protons. When charged particles are moving, they are known as electric
currents.

## Magnetism

> Magnetism is a physical property produced by the _motion_ of electric charge,
> which of course, is the same thing as
> [electric current](Current.md)

A **magnet** is a material or object that produces a magnetic field. This field
is invisible but visible by its effects: pulling on other magnetic materials
such as iron, steel, nickel, cobalt etc and attracting or repelling other
magnets.

All magnets have two ends where their magnetic effects are strongest. These
regions are called the **poles** of the magnet. Materials can be _magnetic_ but
they are not _magnetized_ until another magnetic material has entered into their
field. At this point, the attraction and repulsion behaviour can be observed.

This behaviour is a function of the **magnetic force** which is
**_transmitted_** via the **magnetic field**.

### Relation to electrons

Magnetism, understood as the effect of a magnetic field, arises from the
properties of the electrons in an atom. We know that atoms 'orbit' the nucleus
of the atom but as they circle the nucleus they also spin or rotate on their own
axis.

As they spin they produce a **magnetic dipole**: the two poles noted above. We
call this propensity of electrons the **intrinsic magnetic moment** of the
electron. It is aggregates of these miniature magnetic behaviours that produce
the overall magnetic property of the material.

![](/img/dipole-again.svg)

In most materials, equal numbers of electrons spin in opposite directions. As a
result, their magentic effects are cancelled out. However **in strongly magnetic
materials an overall majority of electrons spin in one particular direction**.
This breaks the equilibrium and produces the magnetic field.

If you have material A where the electrons all spin in one direction and
material B where the electrons all spin in a direction opposite to A, then B
will be attracted to A and you can observe the effects of the magnetic force in
action.

## Fields and forces

### What is a force in physics?

At its most abstract, divorced from the specific types of force, a force is **an
influence that can change the motion of an object**. It is an external agent
capable of changing the velocity of a body with mass. A force has both a
magnitude and a direction.

### What is a field

A field is a property of space. It means that a physical quantity is assigned to
every point in space. This quantity has a numerical value and may vary over
time.

## The electric field

There are different types of field. The electric field is an instance of a
**vector field**. With vector fields there is more than one number for each
point in space:

- a **magnitude**: a size value, i.e. being larger or greater than something
  else
- a **direction**

> The value of the electric field at a point in space equals the force that
> would be exerted on a unit of charge at that position in space.

Every charged object sets up an electric field in the surrounding space. A
second charge “feels” the presence of this field. The second charge is either
attracted toward the initial charge or repelled from it, depending on the signs
of the charges. Of course, since the second charge also has an electric field,
the first charge feels its presence and is either attracted or repelled by the
second charge too. The electric field from a charge is directed away from the
charge when the charge is positive and toward the charge when it is negative.

## The magnetic field

As already noted, the magnetic field is the field created by a magnetic
material: a material where the spin of the electrons is in disequillibrium. As
with the electric field, a magnetic field exerts an attraction or repulsion on
other spinning electrons. This is the **magnetic force**; the force is
transmitted by the field. Attraction occurs when the two sets of electrons spin
in opposite directions to each other. Repulsion occurs when the two sets of
electrons spin in the same direction.

> Crucially the magnetic force influences only those charges that are already in
> motion.

The magnetic field and force is more complex than the electric field/force.
Whereas the electric field and force point either towards or away from the
charge, the magnetic field is different:

- The magnetic field points perpendicular to its source
- The magentic force points perpendicular to the magnentic field

This is illustrated below which shows the magnetic field operating at right
angles to the flow of charge within a wire.

<img src="/home/thomas/repos/eolas/img/magnetic_field.png" width="300" />

## The electromagnetic field

Although we have described the electric and magnetic fields separately, they are
in fact a single unified and inseparable field created by charged particles and
particles with a magentic moment. In describing electricity and magnetism we
have focusing on different attributes of the same phenomenon.

The electromagnetic field does not carry charge or magnetic moment, it carries
energy and momentum. This energy and momentum can be transferred to charged
particles and particles with magnetic moment.

### Maxwell's Equations

The equations express four laws that offer a complete account of the
electromagnetic field. The equations integrate separate discoveries and laws
identified by other scientists with a common mathematical representation. This
is why they are not called 'Maxwell's Laws' since he didn't originate the laws,
he unified them into a common expression. These collective laws capture
everything we have discussed so far in relation to electric and magnetic fields.

1. An electrically charged particle creates an electric field. (Gauss' Law for
   Electricity)
2. Magnetically charged particles do not exist. (Gauss' Law for Magentism)
3. A changing magnetic field creates an electric field. (Faraday's Law of
   Induction)
4. A changing electric field creates a magnetic field. (Ampere's Law)

## The electromagnetic force

Maxwell's Equations describe how electromagnetic fields are generated and behave
but they don't specify how the fields interact with charged particles. An
account of this is provided by Lorentz's force law which specifies what we have
already described above:

> An electric field exerts a forward or backward force on a charged particle and
> a magnetic field exerts a sideways/perpendicular force on a moving charged
> particle.

## Electromagnetic radiation / waves

> Electromagnetic radiation consists in waves of the electromagnetic field
> propagating through space carrying electromagnetic radiant energy.

Electromagnetic waves consist of rapidly changing electric and magnetic fields.
They are emitted any time an electrically charged particle accelerates. These
waves are generally referred to as light. However, more accurately, 'light'
refers to the types of electromagnetic wave that we can see. Electromagnetic
waves form a spectrum based on their frequency and wavelength. For example,
'radio waves' are low-frequency / long wavelength electromagnetic waves and
gamma rays are high-frequency / short wavelength waves:

![](/img/em-spectrum.jpg)

The image below shows the propagation of an electromagnetic wave through space.
We can identify the core components as follows

- The vector of the magnetic field $B$ propagates outwards along the $z$ axis
- The magenetic field is perpendicular to the vector of the electric field $E$
  which propagates upward along the $y$ axis
- The directionality of both waves is forward along the $x$ axis

![](/img/em-wave.gif)

## Using magnetism to generate electricity

## Understand better:

- How do EM waves relate to simple electrical circuits.
- Link discussion here to discussion of Hertz

https://www.britannica.com/science/electromagnetism/Coulombs-law