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“…and then there was light.”
James Clerk Maxwell
Physics 100
Chapt 16
Properties of E & B fields
• Coulomb’s law: E-field lines start on
+ charge & end on – charge
• Ampere’s law: B-fields are produced
by electric currents
• Faraday’s law: Changing B-fields
produce E-fields
• (un-named law): B-field lines never end
In equation form:
E-field lines start on
+charges & end on - charges
B-field lines never end
E-fields are produced by
changing B fields
B-fields are produced by
electric currents
Maxwell
The previous equations, as written, are
mathematically inconsistent with the
conservation of electric charge. He found
he could fix this by adding one more term:
B-fields are produced
by changing E-fields
Maxwell’s equations
B-fields are produced by
changing E-fields
Fields from an electric charge
E
x
E
Is the change in E
instantaneous?
Does it occur only
after some time?
+
M.E.s can tell us?
+
fun in the bathtub
Water level will increase
but not instantaneously
1st waves will propagate
from her entrance point
to the edge of the tub
According to Maxwell’s eqs:
E
x
E
The change in E
is not instantaneous
1st waves made of Efields & B-fields
propagate thru space.
+
+
Wave solutions to Maxwell’s Eqs:

Wave speed =
=

2x9x109Nm2/C2
2x10-7N/A2

=
9x10

=
=
2k
k
9x109+7(m2/C2)xA2
16m2/s2
3x108m/s
k ”strength”
of
electric force
q1q2
Fc = k r2
k = 9.0 x 109 Nm2/C2
k ”strength”
of
magnetic force
FM = k I1I2 l
d
k = 2 x
10-7
N
A2
“…let there be light.”
Maxwell’s equations have
solutions that are waves of oscillating E- &
B-fields that travel at the speed of light.
Faraday & Maxwell made the
immediate (& correct) inference that these
waves are, in fact, light waves.
EM waves
+
+
+
-
antenna
E
B
antenna
E
B
Light wave
B-field
+
E-field
wave velocity
Light wave animation
E
B
Visible light:
Red
Green
Violet
g-rays
X-rays
Ultraviolet
Infrared
micro
waves
TV/FM
AM
radio
waves
Electro-magnetic “spectrum”
l
0.75x10-6m
0.55x10-6m
0.4x10-6m
freq (c/l)
4.0x1014 Hz
5.5x1014 Hz
7.5x1014 Hz