Electromagnetism
Electromagnetism is another of the four fundamental interactions. Like gravity, It also has long range but it is much
stronger than Gravity and the Weak interaction. However, the
Electromagnetic interaction is weaker than the Strong interaction.
• Electric Charges and Atoms: There are two kinds of
electric charge, (+) and (-). The unit of charge is the Coulomb,
which is the charge transported by a current of 1 Amp flowing
for one second. Opposite charges attract and like charges repel.
Two charges q1 and q2 separated by a distance r attract or repel
with a force of magnitude.
F =
kq1 q2
r2
Electric charge is conserved. The proton has a charge +e and
the electron has −e, where e = 1.6×10−19 Coulombs. An atom
consists of a nucleus with protons and neutrons, with electrons
in orbit around the nucleus. In a neutral atom, the number of
electrons in orbit is the same as the number of protons in the
nucleus. The electrons are kept in orbit because the protons
attract them. The proton repel each other but the nucleus is
not destroyed because the Strong Force keeps them together.
An atom with a nucleus that has Z protons and N neutrons is
symbolized as Z+N
X , where X is the chemical symbol, so for
Z
12
example 6 C is a stable carbon nucleus with 6 protons and 6
neutrons, but 14
6 C is an unstable (radioactive) isotope of carbon. In the periodic table the atomic number is the same as Z.
99.3% of natural uranium is 99.3% is the isotope 238
92 U , which
is not bomb material. The other 0.7 % is the isotope 235
92 U ,
which is bomb material (fissionable), and must be separated
(or enriched) by centrifuge methods from the 238
92 U isotope.
• Electric Fields:
An electric charge q that experiences an electric force F~ is said
~ due to all the other
to be immersed in the electric field E
~ Since a positive charge
charges in the world, where F~ = q E.
repels another positive charge, we see that the electric field
produced by it is radially away from itself.
E
+
The electric field around a positive (+) electric charge
points radially outward, away from the (+) charge. The
field field around a (-) charge points inward toward the
charge.
The electric filed produced by two equal and opposite charges
(an electric dipole) is more complicated, as shown below.
Electric filed of two equal and
oppsite charges, an electric dipole
E
-
+
Electric field lines start at the (+) charge and end at the (- )
charge. They form closed loops because electric momopoles
(isolated charges) do exist.
Two uniformly charged parallel metal plates produce a uniform
electric field as shown below. This is useful in many devices,
such as oscilloscopes, and ink jet printers. The field produced
by a battery is also shown.
Uniform electric filed E between two parallel metal plates.
The electric filed always points from positive to negative.
++++++++++++++++++++++++++++++++++++
E
--------------------------------------------
A battery
+
-
• Voltage Difference and Power:
When an electric charge q moves in an electric field, the field
does work on the charge. We say that the charge has moved
across a voltage difference V , where the work W = qV . For
example, a 3 Coulomb charge that moves across 1.5 Volts, has
had 4.5 Joules of work done on it by the field. The voltage
difference is roughly equal to the electric field multiplied by
the distance moved, so V ≈ Ed. A battery is capable of maintaining charges on its terminals even if an electrical current is
allowed to flow by connecting its terminals to each other using
wires. The battery actually maintains an electric field and a
rated voltage difference between its terminals. The energy for
this comes from chemical reactions in the battery. The electric
plug in the wall has a voltage difference of 120 Volts. When a
current i = 2 Amps (or 2 Coulombs per second) flows, the work
is 120 Volts × 2 Coulombs/second=240 Joules/second, or 240
Watts, so that Wattage, or Power P equals current×Voltage,
that is P = iV . The energy for this comes from the electrical
generators of the power company. A large city power plant can
generate a gigawatt, or a million kilowatts. On a sunny day,
the solar energy that falls on an area of 1 squared kilometer is
more than 1 gigawatt.
• Magnetic Fields:
Magnets are dipoles because they have two poles. Two North
poles repel, Two South poles also repel, but a North and South
pole attract. The magnetic field is explored using a compass
needle. The magnetic field B comes out of the North pole of
the magnet and goes into the south pole, but the field lines
form closed loops because magnetic monopoles do not exist. If
we cut a magnet in half to try to isolate a pole, we get two
smaller dipoles.
Like poles repel
S
N
N
S
S
N
Force
S
N
Opposite poles
attract
B
A magnet is a magnetic dipole.
S
N
Magnetic field lines come out of the North pole and go into the
South pole, but they form closed loops because magnetic
monopoles do not exist. Cut a magnet in half, and you still get
two dipoles.
S
S
N
N
S
N
The North pole of a magnet is the North
seeking pole. Since opposite poles attract,
the geographic North pole of the Earth is a
magnetic South pole.
North
America
Europe
B
Equator
N
S
The direction of the magnetic filed B is defined as the
direction taken by a compass needle. So, a compass
needle is used to examine a B filed because the needle
lines itself up with the B field.
S
N
B
Since the North seeking pole of a magnet points approximately
to geographic North, it turns out that the Earth acts as a sort
of magnet, with a South magnetic pole near the Earth’s geographic North pole. Ultimately, magnetic fields are produced
by electric currents. The Earth does not have a gigantic bar
magnet, rather the magnetic filed of the Earth is due to electrical currents in its molten iron core. In the case of a magnet,
these are atomic currents.
• Electric Currents Produce Magnetic Fields:
Electric current is the flow of electric charge. An electrical
current of I Amp flowing in a long straight wire produces the
magnetic filed shown, whose lines go in circles around the wire,
with a magnitude
µ0 I
2πr
B=
current coming out of
the paper
B
I
r
B
current I
current toward the right
A coil of wire with a current (a solenoid) can produce a strong
magnetic filed similar to that of a bar magnet as shown below.
A coil of wire with current I
B
side view
I
I
front view
B
• Magnetic Fields Exert Forces Upon Electric Currents
Current I into the paper
I
Magnetic field B
F
to the left
I
MAGNETIC FIELD EXERTS A FORCE ON A CURRENT
B down
•Changing Magnetic Fields Generate Electric Fields
FARADAY’S LAW OF ELECTROMAGNETIC INDUCTANCE:
CHANGING MAGNETIC FIELDS INDUCE ELECTRIC FIELDS
Induced electric field E
E
Induced electric current I
loop of wire
Magnetic field B increasing
•Changing Electric Fields Generate Magnetic Fields
• Electromagnetic waves:
The fact that changing magnetic fields generate electric fields,
and that in turn, changing electric fields generate magnetic
fields, makes it possible for electromagnetic waves to travel
through empty space. Electromagnetic waves travel in all directions, so their wave fronts are spheres. Their amplitude
represents the strength of the electric field. Their intensity,
which is proportional to the square of the amplitude, falls as
1/r2 because the energy is spread over a sphere of radius r. In
a vacuum all electromagnetic waves, radio, microwave, light,
X-rays, etc., all travel with the speed of light c = 3 × 105 km/s,
which is actually the fastest speed possible in the universe. An
electromagnetic wave consists of oscillating electric fields transverse to the direction of propagation, shown in red in the figure
below, together with magnetic fields, shown in blue, that are
also transverse and perpendicular to the electric fields.
We say that such a wave is vertically polarized. An electric
dipole antenna is shown in the figure below. The antenna radiates strongly in a direction perpendicular to the antenna and
very weakly in the direction along the antenna wires. A vertical electric dipole antenna produces a vertically polarized wave
as shown above. The horizontal dipole antenna produces a
horizontally polarized wave.
Electric dipole antenna
direction of strong wave perpendicular to antenna
oscillating voltage
wire
zero radiation in this
direction prallel to antenna
zero radiation in
this
direction parallel to antenna
λ/2
• Polarization of Light:
Visible light is emitted by atoms. In ordinary light sources the
electric field changes direction randomly, because the atoms
radiate independently of each other, and we say the light is
unpolarized. This is why our eyes have not evolved to detect
the polarization of light. However reflected light, and blue sky
light are partially polarized. Polarized sunglasses shown below
have a polarizing filter that only allows vertically polarized light
to pass through.
vertically polarized light passes through and enters eyes
pass axis
absorption axis
polarizing filter
horizontally polarized light is absorbed and does not pass
vertical incoming E
field
vertical E field
passed
horizontal
incoming E field
horizontal E field
absorbed and does
not pass
polarizing filter
pass axis
They are useful because they tend to eliminate the glare produced by light reflected from horizontal surfaces. If a vertical
filter is put in front of a horizontal filter, then no light passes
through at all. The polarization of light is used in a clever way
to produce the bright and dark pixels in LCD (liquid crystal
display) TV and computer monitors.