Download Lecture #34 Tutorial on electric potential, field, and light

564-17 Lec 34
Mon. 10Apr17
Tutorial on potentials, fields, and light
= electric potential (volt)=Joules/Coulomb
generated by a charge q in coulombs
at a distance r in meters:

q
4 0 r
J /C
Where 0 = "the electric constant" or
"vacuum permittivity" or
"permittivity of free space"
electric field (volt/m)
generated by a charge q at a distance r in meters:

q
4 0 r
2
V /m
electrostatic energy of two charges at
distance r apart: Coulomb's Law
q1q2
U
 1q2  joules
4 0 r
If q2 = 1.602 x 10-19 C = e and 1= 1 volt
U = 1.602 x 10-19 J = 1 eV
Coulomb's Law (Force)
q1q2
F
 newtons (N)
2
4 0 r
This is also the force on q2 due to the electric field
of q1: F  1q2  newtons (N) 

Noting that F and field are vectors F   q
Convention is that a positive x-field pushes a positive
charge in the + x direction.
The change in potential energy when a charge
is moved a distance r in a constant electric field
is given by:
q1q2
V 
r  force  distance  qr
2
4 0 r
This is also the energy of a dipole in a constant
electric field: where qr = m = the dipole
Some Reference Points
For an elementary charge, e the potential at 1 Å distance =
9 E 9(1.602 10 19 )


 14.4 volts
10
4 0 r
1.0 10
e
and the electric field is:
9 E 9(1.602 10 19 )
10



14
.
4

10
volts/m
2
 20
4 0 r
1.0 10
e
 14.4 10 volts/cm
8
In proteins, electric fields on the order of 5 x 107 V/cm
are common, and can shift emission wavelengths by 50 nm.
What exactly is the "electric constant", 0 ???,
sometimes called the vacuum permittivity.
It is that number which gives the correct force2
between two electrons, i.e., makes F  e
true.
2
4

r
 0  8.854187817620... × 10-12 C 2 ·N -1·m -2 0
1
0 
2
0c
0 is the "magnetic constnant" called the
vacuum permeability
 0  4 × 10-7 Henry/m  4 × 10-7 JA -2 m -1
1
4 0
 8.98755 10  9E9  c 10
9
2
7
This nice number is also known as ke , the Coulomb constant
The fine structure constant 
•e is the elementary charge;
•π is the irrational number pi;
•ħ = h/2π is the reduced Planck constant;
•c is the speed of light in vacuum;
•ε0 is the electric constant or permittivity of free space;
•µ0 is the magnetic constant or permeability of free space;
•ke is the Coulomb constant;
•RK is the von Klitzing constant;
•Z0 is the vacuum impedance or impedance of free space.
The definition reflects the relationship between α and the elementary
charge e, which equals √4παε0ħc.
Richard Feynman, one of the originators and early developers of the
theory of quantum electrodynamics (QED), referred to the fine-structure
constant in these terms:
There is a most profound and beautiful question associated with the observed
coupling constant, e – the amplitude for a real electron to emit or absorb a real
photon.
It is a simple number that has been experimentally determined to be close to 0.08542455.
(My physicist friends won't recognize this number, because they like to remember it as the
inverse of its square: about 137.03597
with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever
since it was discovered more than fifty years ago, and all good theoretical physicists put
this number up on their wall and worry about it.) Immediately you would like to know
where this number for a coupling comes from: is it related to pi or perhaps to the base of
natural logarithms?
Nobody knows. It's one of the greatest damn mysteries of physics: a magic
number that comes to us with no understanding by man. You might say the "hand of
God" wrote that number, and "we don't know how He pushed his pencil." We know what
kind of a dance to do experimentally to measure this number very accurately, but we don't
know what kind of dance to do on the computer to make this number come out, without
putting it in secretly!
— Richard Feynman, Richard P. Feynman (1985). QED: The Strange Theory of Light and
Matter. Princeton University Press. p. 129. ISBN 0-691-08388-6.
absorption
emission
repulsion
Perturbation from Light (dipole approximation)



H '  W   0 cos(t ) • m (or  )
for plane-polarized light, polarized in the x
direction for an electron:
 2
2
2
2
| W fi |  |  0, x | | ex fi | (or |  fi , x | ),
where  fi , x  electric dipole transition moment
and x is the position of the electron