Lecture 2: Classical Physics September, 2000 1

LECTURE 2 – CLASSICAL PHYSICS

All of classical physics (what was know before 1905) can be summarized in a single table:

• Maxwell’s Equations • Conservation of charge (can be deduced from Maxwell’s equations) • Force laws • Laws of motion • Law of gravitation

1. Maxwell’s Equations:

Gauss’s Law – Electric and Magnetic

The source of electrical field is the electrical charge

0) surface closed a through B of(flux 0 ==Β⋅∇&

There is no magnetic monopole Faraday’s law

A changing magnetic field induces an electric field

Ampere’s Law

it) through Eflux of change

of rate loop/rough current th loop a around B of (integral o2 +=

∂Ε∂+=Β×∇ ε

εο t

jc

*&

A current or time varying field induces a magnetic field

In free space these can be expressed as a wave equation:

it) through B offlux of change of rate - loop a around E of (integral - =Β∂∂=Ε×∇

&*

t

)inside/ charge surface closed a through E of(flux / ooE εερ ==⋅∇*

01

2

2

2

2 =∂∂−∇

t

E

cE

Lecture 2: Classical Physics September, 2000 2

2. Conservation of charge:

3. Force on a charge

4. Law of motion

5. Gravitation

Operators

)(x

)()(

)(

)()(

2

VectorurlV

VScalerapacianV

ScalerivergenceV

VectorradientV

C

L

D

G

*

*

∇∇⋅∇∇

⋅∇∇

in time) charge of change equals flow Charge of e(Divergenc - j t∂

∂=⋅∇ ρ

( ) Law) (Lorentz q F Β×+Ε=**&&

ν

( )

ma

momentum) theis (p c / - 1

m p

dt

d

22

=

==

F

pFν

ν

kji ˆz

ˆy

x

:ex z

k y

j x

i ∂∂+

∂∂+

∂∂=∇

∂∂+

∂∂+

∂∂=∇ νννν

G- 2

21

r

mmF =&

Lecture 2: Classical Physics September, 2000 3

6.0 Problems with these equations

These simple laws with extensions and modifications were found to correctly predict a vast array of effects and properties. However, a number of effects became experimentally confirmed that could not be explained by these classical theories. Three of the most prominent were:

(a) Black body radiation (b) Heat capacity of solids (c) The photoelectric effect.

We shall use the photoelectric effect as an example. Photoelectric effect If light of a frequency, f, is incident on a solid electrons are emitted from the surface:

∼ f e It was found experimentally that electrons are only emitted when fo is the threshold light frequency, φ is a function of the material (called the work

function), and h is Plank’s constant, a fundamental constant of physics (like π which is a fundamental constant of geometry). The photoelectric effect is independent of the intensity of the light striking the solid sample for frequencies below fo. The existence of the threshold frequency cannot be explained on the basis of classical physics. The classical analysis was: if light is just a classical EM wave then the energy delivered to the solid should be dependent on the intensity and the more energy delivered the more electrons should be emitted. This seemed to be wrong! Einstein proposed an explanation of this phenomenon. He proposed that the energy of the light be carried in a particle. He called this particle a photon. He also proposed that the energy of photon was proportional to its frequency and we have,

ππωφω h/2 f2 o ==> !!

ω! =Ε p

Lecture 2: Classical Physics September, 2000 4

Einstein’s model to explain the photoelectric effect.

Thus only when a photon with energy greater than the work function of the metal (the amount of energy needed to remove an electron from a solid) collided with an electron was there enough energy to emit an electron. This explained the behavior of the solid when illuminated. If the energy of a photon were less than the work function then no electrons would be emitted. However, if Ep > φ then an electron can be emitted and the difference in energy will be equal to the kinetic energy of the emitted electron. It was also proposed that if an electromagnetic field can behave like a particle with an energy of EP, then the light particle should also have a momentum p.

This can be derived from relativistic equations and is determined assuming that the photon has zero mass and travels at the speed of light.

This was the start of Quantum Mechanics! Example of another effect classical physics can not explain. Plasma Glow – place a gas in a glass tube, use a large electric potential to cause break down (separation of ions and electrons). The light emitted is only at certain wavelengths. – A mystery remains: why are there spectral lines? A related question is why don’t electrons collapse into a nucleus? + V wavelength of spectral gas at low pressure light intensity lines depends on gas glow discharge light λ λ1 λ2 λ3

)only! photons(for c / k ω== kp !

Lecture 2: Classical Physics September, 2000 5

Complementary Notes.

The divergence of a vector flux density (B, D) is the outflow of flux from a small closed surface per unit volume. It tells us how much flux is leaving a small volume on a per unit-volume basis.

Charges are the sources (+) and sinks (-) of electric field. If in the previous figure there is a difference between the amount of flux flowing into and out of the closed surface A, it will be due to the presence of sources or sinks within A. There is no magnetic counterpart to the electric charge, i.e., no isolated magnetic poles have ever been found. Unlike E, B does not diverge from or converge toward some kind of magnetic charge (a monopole source or sink). Lines of B are themselves continuous and closed, thus, there would be an equal number of lines of B entering and emerging from A.

E, B

Lecture 2: Classical Physics September, 2000 6

The curl can be described as the circulation of a vector field per unit area.

A time varying B generates a circulating E.

A current flow (i) or time varying E induces a magnetic field. Note that E affects B and B will in turn affect E. Thus, E and B can be considered as two aspects of a single physical phenomenon, the Electromagnetic Field.

B

E

Lecture 2: Classical Physics September, 2000 7

Black Body Radiation: Radiation emitted by an opaque or hot body.

Black Body Radiation Curves.

Classical physics failed in explaining the form of these intensity curves. The best approximation (Rayleigh-Jeans law) matched the experimental curves only in the very long wavelength region and predicted infinite power in the short wavelength region (absurd!).

Heat Capacity: Rate of increase of internal energy per unit temperature rise.

Ra

dia

nt

Flu

x D

ens

ity