Transcript Gauss`s law

Knowledge of Light
By
Prof. Larry Zhongxin Shen
Graduate University of Chinese Academy of Sciences
July 02, 2012
What is light?
In the late 1600’s Newton explained many of
the properties of light by assuming it was
made of particles.
”Tis true, that from my theory I argue the corporeity of
light; but I do it without any absolute positiveness…”
Because of
Newton’s
enormous
prestige, his
support of the
particle theory of
light tended to
suppress other
points of view.
“The waves on the surface of
stagnating water, passing by the
sides of a broad obstacle which
stops part of them, bend afterwards
and dilate themselves gradually into
the quiet water behind the obstacle.
But light is never known to follow
crooked passages, nor to bend into
the shadow.”
In 1678 Christian Huygens
argued that light was a pulse
traveling through a medium,
or as we would say, a wave.
I’m
thinking
waves.
Newton’s Corpuscular Theory
• Newton did not specifically say that light had to be
particles. He did describe many of the properties of
light in terms of particles including refraction, and
reflection.
• He did not see evidence for wave properties such as
interference, and as in this quote, diffraction. This
lead him to favor particles.
• Newton’s reputation kept the physics community from
seriously considering light as waves for about 100
years. It seems that very little research was done
during that time to actually resolve the issue.
In 1803 Thomas Young’s double slit experiment showed that, much like
water waves, light diffracts and produces an interference pattern.
Light must be
waves!
=2dsin
Young’s Experiment
•
Young first experimented with a pinhole and sunlight and saw interference
fringes. In 1816 Fresnel wrote a paper looking at light in terms of waves and
predicting such effects as diffraction and interference. He was disappointed to
hear that Young had already reported these effects.
•
In 1818 the French Academy’s annual competition concerned diffraction and
interference effects and hoped to obtain convincing evidence for a corpuscular
theory. In response to the challenge Fresnel showed that the shadow behind a
small sphere would have a bright spot at its center.
•
Young’s original double slit experiment was done with double pin holes. The
sketch of the production of the interference pattern was done by Young.
•
This is a good time to get out the ripple tank if you have not already done so. I
also like to demonstrate interference with microwaves and sound.
“…it seems we have strong reason to
conclude that light itself is an
electromagnetic disturbance in the form of
waves propagated through the
electromagnetic field according to
electromagnetic laws.”
In the 1860’s Maxwell, building on Faraday’s
work, developed a mathematical model of
electromagnetism. He was able to show that
these electromagnetic waves travel at the
speed of light.
Classical Physics Time
Maxwell（1831-1879）
We are standing on
the Giant’s shoulders.
Maxwell is one of them.
Conceptual Description
• Conceptually, Maxwell's equations describe how electric
charges and electric currents act as sources for the electric and
magnetic fields. Further, it describes how a time varying electric
field generates a time varying magnetic field and vice versa.
(See below for a mathematical description of these laws.) Of the
four equations, two of them, Gauss's law and Gauss's law for
magnetism, describe how the fields emanate from charges. (For
the magnetic field there is no magnetic charge and therefore
magnetic fields lines neither begin nor end anywhere.) The other
two equations describe how the fields 'circulate' around their
respective sources; the magnetic field 'circulates' around electric
currents and time varying electric field in Ampère's law with
Maxwell's correction, while the electric field 'circulates' around
time varying magnetic fields in Faraday's law.
Gauss's Law
• Gauss's law describes the relationship between an
electric field and the electric charges that cause it:
The electric field points away from positive charges
and towards negative charges. In the field line
description, electric field lines begin only at positive
electric charges and end only at negative electric
charges. 'Counting' the number of field lines in a
closed surface, therefore, yields the total charge
enclosed by that surface. More technically, it relates
the electric flux through any hypothetical closed
"Gaussian surface" to the enclosed electric charge.
Gauss's Law for Magnetism
• Gauss's law for magnetism states that there are no "magnetic
charges" (also called magnetic monopoles), analogous to
electric charges.[1] Instead, the magnetic field due to materials
is generated by a configuration called a dipole. Magnetic dipoles
are best represented as loops of current but resemble positive
and negative 'magnetic charges', inseparably bound together,
having no net 'magnetic charge'. In terms of field lines, this
equation states that magnetic field lines neither begin nor end
but make loops or extend to infinity and back. In other words,
any magnetic field line that enters a given volume must
somewhere exit that volume. Equivalent technical statements
are that the sum total magnetic flux through any Gaussian
surface is zero, or that the magnetic field is a solenoidal vector
field.
Geomagnetic Storm
Faraday's Law
• Faraday's law describes how a time varying
magnetic field creates ("induces") an electric field.
This aspect of electromagnetic induction is the
operating principle behind many electric generators:
for example, a rotating bar magnet creates a
changing magnetic field, which in turn generates an
electric field in a nearby wire. (Note: there are two
closely related equations which are called Faraday's
law. The form used in Maxwell's equations is always
valid but more restrictive than that originally
formulated by Michael Faraday.)
Ampère's Law with
Maxwell's Correction
• Ampère's law with Maxwell's correction states that
magnetic fields can be generated in two ways: by
electrical current (this was the original "Ampère's
law") and by changing electric fields (this was
"Maxwell's correction").
• Maxwell's correction to Ampère's law is particularly
important: it shows that not only does a changing
magnetic field induce an electric field, but also a
changing electric field induces a magnetic field.[1][2]
Therefore, these equations allow self-sustaining
"electromagnetic waves" to travel through empty
space (see electromagnetic wave equation).
Magnetic Core Memory
Speed of Light
• The speed calculated for electromagnetic
waves, which could be predicted from
experiments on charges and currents,[note 1]
exactly matches the speed of light; indeed,
light is one form of electromagnetic radiation
(as are X-rays, radio waves, and others).
Maxwell understood the connection between
electromagnetic waves and light in 1861,
thereby unifying the theories of
electromagnetism and optics.
Electromagnetic Spectrum
氢原子巴耳末系的发射光谱
图中的每一根谱线均可由氢原子中电子允许的能
量公式来解释。在氢原子中，从n=3, 4, 5, 6, 7
至n=2能级的跃迁涉及到对应的光子。 这些转变
是巴耳末第一个发现的，被称为巴耳末系列。
氢原子的光谱与能级
其中，n是主量子数，为正整数。如果电子的是
n=1的状态，能量为-13.6电子伏特 ，这是基态的
能量。如果电子的是在n=2的状态，能量为-3.4伏
特，这被称为第一激发态的能量。
Spectroscopy
E1
Bohr frequency condition
hn = E1 – E2
Absorption
spectroscopy
Emission
spectroscopy
E2
Wavelength:

c
n
n
Wavenumber: n~ 
c
(cm-1)
单光子的能量公式
其中，h为普朗克常数。由此公式可以计算每一根
谱线的频率ν和波长λ。
Light is an EM Wave
• If light is a wave, then what is waving? In 1845 Faraday showed
that light traveling through a thick piece of glass had its plane of
polarization rotated by a magnetic field applied to the glass.
This convinced Faraday that light was somehow related to
electricity and magnetism. Faraday lacked the math skills
needed to develop his theory of lines of force into a
mathematical theory of electromagnetic waves. Maxwell went
beyond the work of Faraday to present the new idea that an
electric field that is changing in time must be accompanied by a
magnetic field. It is not just currents in conductors that produce
fields but changing electric fields in any medium, including
empty space.
• Maxwell did not live to see the experimental verification of his
theory by Hertz in 1888.
Boltzmann Distribution
Boltzmann’s Sculpture in the Front of
the Main Building ,Vienna University
I don’t like that!
In 1900 Max Planck was able to
explain the spectrum of a
“blackbody” radiator by assuming
that light energy is quantized.
That quantum of light energy was
later named a photon.
E=hf
E=hf+
A few years
later, in 1905,
Einstein used
Planck’s idea to
explain the
photoelectric
effect.
That quantum
of light energy
seems
particle-like!
Quantum Physics Time
Max Planck，18581947), 1918 Nobel
Physics Prize.
If you did not
understand light is
one form of
electromagnetic
radiation, you
would ,get laser.
Comparison of Three Theories
Einstein (1879-1955)，1921
Noble Physics Prize
阿尔伯特爱因斯坦（Albert
Einstein）的数学描述如何
通过光电效应引起的量子（
现在称为光子），是他在一
篇名为“关于光量子的生产
和转化”（他在1905年的论
文之一）中提出的。爱因斯
坦的工作预见了光电子的能
量随入射光的频率线性地增
加。直到1915年，罗伯特安
德鲁密立根（Robert
Andrews Millikan）发现，
爱因斯坦的预见是正确的。
爱因斯坦对光电效应的解释
使他赢得了1921年的诺贝尔
物理学奖。