Where 0 = "the electric constant" or"vacuum permittivity" or

"permittivity of free space"

Tutorial on potentials, fields, and light

= electric potential (volt)=Joules/Coulomb

generated by a charge q in coulombsat a distance r in meters:

CJr

q/

4 0

564-17 Lec 34Mon. 10Apr17

electric field (volt/m) generated by a charge q at a distance r in meters:

mVr

q/

4 2

0

If q2 = 1.602 x 10-19 C = e and 1= 1 voltU = 1.602 x 10-19 J = 1 eV

electrostatic energy of two charges at distance r apart: Coulomb's Law

joules4

21

0

21 qr

qqU

(N) newtons4 2

0

21 r

qqF

This is also the force on q2 due to the electric field of q1: (N) newtons21 qF Noting that F and field are vectors qF

Convention is that a positive x-field pushes a positive

charge in the + x direction.

Coulomb's Law (Force)

The change in potential energy when a chargeis moved a distance r in a constant electric fieldis given by:

qrrr

qqV

distance force

4 2

0

21

This is also the energy of a dipole in a constantelectric field: where qr = m = the dipole

For an elementary charge, e the potential at 1 Å distance =

Some Reference Points

volts4.14100.1

)10602.1(99

4 10

19

0

E

r

e

and the electric field is:

volts/cm104.14

volts/m104.14100.1

)10602.1(99

4

8

10

20

19

2

0

E

r

e

In proteins, electric fields on the order of 5 x 107 V/cmare 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 forcebetween two electrons, i.e., makes true.

729

0

-1-2-7-7

0

1010 8.987554

1

mJA 10 × 4Henry/m 10 × 4

c9E9

2

0

2

4 r

eF

2

0

0

-2-12-12

0

1

·m·NC10 × 7620...8.85418781

c

0 is the "magnetic constnant" called the vacuum permeability

This nice number is also known as ke , the Coulomb 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.

The fine structure constant

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.

absorptionemission

repulsion

Perturbation from Light (dipole approximation)

)or ()cos(' 0

mtWH •

for plane-polarized light, polarized in the xdirection for an electron:

electron theofposition theis x and

momentn transitiodipole electric where

),||or (||||||

,

2

,

22

,0

2

xfi

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