Electricity + Magnetism + Optics

Electrodynamics' place in the context of the rest of physics.

Rumble of the forces

We know about four different forces...

    Gravity / Electric / Strong / Weak

Note that magnetism is not in the list...

How do these compare with each other?

Coulomb's law

The whole first half of the course might be summarized by Coulomb's law which specifies the force between two charges: $$ \myv F = \frac{1}{4\pi\epsilon_0}\frac{q_1 q_2}{\rr ^2}\uv \rr$$

We'll use SI units -- meters, kilograms, seconds, Newtons -- in which charge is in Coulombs.

The permittivity of free space is $\epsilon_0= 8.85\times 10^{-12}C^2/(Nm^2)$.

$q_1$ and $q_2$ are the charges on the two "point-like" charges at positions $\myv r$ and $\myv r'$ where their relative separation is $\myv \rr = \myv r-\myv r'$. The charge of an electron is ~$-1.6\times 10^{-19}$ C.

E compared to gravity

Compare the magnitude of the electric and gravitational forces between two electrons which are 1 m apart from each other...
The mass of an electron is $9.1 \times 10^{-31}$ kg, and $G=6.67\times10^{-11} N\cdot m^2/kg^2$.

$$\begineq F_e&=&\frac{1}{4\pi\epsilon_0}\frac{q_1 q_2}{\rr^2}\\ &=& \frac{(-1.6\times 10^{-19} C)^2}{4\pi \left[8.85\times 10^{-12}C^2/(Nm^2)\right] 1m^2}=2.3 \times 10^{-28}N\endeq$$

$$\begineq F_g &=& G\frac{m_1m_2}{\rr^2}\\ &=&6.67\times10^{-11}N m^2 / k g^2 \frac{(9.1 \times 10^{-31} k g)^2} {1m^2}=5.5\times10^{-71} N\endeq$$

$\frac{F_e}{F_g} \approx 10^{42}$ : Looks like the electric force is much stronger than gravity.

What gravity?

How is it that we are even dimly aware of gravity if the electric force is so much stronger?

Any amount of positive charge attracts negative charge to itself (and vice versa), until the amount of positive and negative charge in any macroscopic body is very nearly equal.

E compared to nuclear forces

The nucleus

At the heart of an atom is the positively charged nucleus surrounded by a cloud of electrons.

Is there anything about this picture that makes you uncomfortable?

Like the fact that those protons aren't flying away from each other?

The strong force

The "strong" force is...
  • stronger than the electric force.
  • stronger than gravity.
  • attractive between any combination of protons and neutrons.

If you're so strong...

If the strong force is so strong, why don't *all* the protons and neutrons in the world universe stick together?

In fact, every nucleus with an atomic number greater than 83 is unstable (that is, radioactive) -- ${}_{83}^{209}$Bi is the largest stable nucleus.
  • $F_s \propto e^{-\beta r}$ -- vector bosons with mass.
  • $F_e \propto 1/r^2$ -- vector boson (photon) with no mass.
  • Strong > E at small distances, but range is $\approx 1/\beta$.
  • E > Strong at large distances.

The strong force (as well as the "weak" force) is short-range. The proof is the limited size of the periodic table.

The Electric force turns out to be the most important for many parts of every-day experience:

  • Chemistry is all changes in the configurations of electrons.
  • The contact forces that arise when we push on objects are ultimately electrical.

Charge

Electrical charge....

  • comes in two flavors, which we call + and - (plus and minus).
  • appears to be precisely conserved in the universe: both globally and locally.
  • Charge is quantized. The charge of any macroscopic body is only ever $Q= n e$: a positive (or negative) multiple of $e$, the charge on the electron.
  • Why is the charge of the electron--a pointlike "lepton"--precisely the same magnitude (though opposite sign) of a compound "baryon" like the proton (made up of three quarks)?

Unification of theories

The following three subjects were considered separate realms of physics before ~1800:

Magnetism

Ancient Indians, Greeks and Chinese (at least) were aware of the singular properties of lodestone (magnetized magnetite): of how it attracted other lodestones, as well as iron.

By the 11th century, the Chinese were using suspended "floating fish": magnetized needles or pieces of iron floating on water as to keep track of direction at night or with low visibility. The Ming dynasty diagram shows the names for different compass headings.

Electricity


Electricus is Greek for 'amber-like'.

~600 BC: Thales of Miletus observed that amber rubbed with cat's fur could attract light objects. (He believed this was induced 'magnetite-ism'.)

Other electrical phenomena: static electricity generators, the two varieties of charge, current as a flow of charge, batteries, conductors and insulators.

Optics

Newton argued that light consists of particles. Thomas Young showed ~1800 with his slit experiments, that light acts as a wave.

Optical phenomena included the reading stones invented by Abbas Ibn Firnas in the 9th century, spectacles invented in the 13th century, Galileo's telescope, the splitting of the sun's light via a prism.

At right, detail from Death of the Virgin by the Master of Heiligenkreuz, early 15th century.

Unification

  • 1820. Oersted notices that an electric current causes a magnetic needle to change direction.
  • 1831. Faraday finds that a moving magnet can cause an electric current to flow.
  • 1864. James Clerk Maxwell combined electric and magnetic equations into one theory of "electromagnetism", that also implied traveling waves in the electric and magnetic fields.

These waves travel with velocity $c$, and turned out to be light.

20th century

Are the E-M fields just an accounting device for keeping track of the force that one bunch of charge exerts on another bunch?

We say the interference of E-M waves is what accounts for...

The interference pattern of a double-slit apparatus--detected as individual particle (photon) impulses.

QED sez: Waves of the E-M field are the probability amplitudes associated with the Q-M field quanta: photons.

In summary...

  • Maxwell's theory unifies electricity, magnetism, optics.
  • The theory was already relativistic before relativity.
  • The theory gave the same results as quantum field theories before quantum mechanics: The photon is the massless quanta of the electromagnetic field.

Image credits

Ming dynasty compass diagram, Matthew Sullivan