Download Lecture 11

Electromagnetism
Ch. 8
1865: James Clerk Maxwell
1887: Heinrich Hertz
Completed the theory
of electromagnetism
(Maxwell’s equations).
Generated and detected
electromagnetic waves.
The equations predicted
electromagnetic waves.
Electromagnetic waves
• The electric and magnetic fields E and B oscillate
(red and blue arrows).
• Electric and magnetic fields are perpendicular to
the propagation direction (transverse wave).
• The wave travels at the velocity of light c.
• c = 3·108 m/s = 1 foot/ns in empty space.
Ch. 9.4
Electric field and charge
• The electric field is the electric force acting on a
charged particle, divided by the electric charge.
• The electric force is similar to the gravitational
force (next slide).
• The electric charge is analogous to mass in gravity.
But charge can be positive or negative while mass is
always positive. And charges repel each other while
masses attract each other.
• The electric field exists everywhere in space, like a
wave.
Ch. 8.1
Electric vs. gravitational force
Electric and gravitational forces obey similar laws:
Felectric =
Fgravity =
G e
G 
q 1  q2
d2
m1  m2
Coulomb
Newton
d2
d = distance, q = charge, m = mass
The atom as planetary system
Ch. 8.2
Opposite charges of protons (blue) and
electrons (black) produce an attractive
force similar to the gravitational force
between the Sun and the planets.
Electric vs. gravitational force
• The electric force between two electrons is
1042 times larger than the gravitational force.
• Why is gravity so weak ?
• We don’t know.
• Theorists are trying to understand this by adding an
extra dimension to space. The idea is that the source
of gravity lies far away in the 4th space dimension and
becomes attenuated this long distance. We can see
only three space dimensions and are puzzled by that.
The elementary charge
• Charge comes in multiples of e, the elementary charge.
This is also called charge quantization.
• The charge of a proton is +e , that of an electron is –e.
• Mass, the analog of charge in gravity, is not quantized ,
i.e., particle masses are not multiples of one mass unit.
• The Standard Model of particle physics cannot explain
why charge is quantized.
The electromagnetic coupling constant 
• The square of the elementary charge e in Coulomb’s law is
the electromagnetic coupling constant .
It measures the strength of the electromagnetic interaction.
• In fundamental units,  becomes:
 = e2/ћc 
1
137
• This number has mystified physicists for almost a century.
• If  had a slightly different value, we would not be around:
The energy production of the Sun depends strongly on
, because the electric repulsion of two protons is the
bottleneck of the fusion reaction that powers the Sun.
Chemical energies depend on 2 . Chemistry would be
very different.
Electric vs. magnetic fields
Electric
Magnetic
Iron filings near a bar magnet.
Electric vs. magnetic fields
Ch. 8.5, 8.6
Electric
Magnetic
Electric monopole field
Magnetic dipole field
Field lines converge onto one center.
Field lines converge onto two centers.
Magnetic field and current
Ch. 8.3
• While the electric field originates from charges, the
magnetic field originates from currents.
• The electric current is defined as charge per second.
The current unit is Ampere (A).
The charge unit is Coulomb (C) = A  s .
• The magnetic field of a bar magnet originates from
currents inside atoms.
Maxwell’s equations
1) Charges cause electric fields.
2) Currents cause magnetic fields.
3) Changing electric fields cause magnetic fields.
4) Changing magnetic fields cause electric fields.