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 J / C 40r 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 2 V / m 40r electrostatic energy of two charges at distance r apart: Coulomb's Law q1q2 U 1q2 joules 40r -19 If q2 = 1.602 x 10 C = e and 1= 1 volt U = 1.602 x 10-19 J = 1 eV Coulomb's Law (Force) q1q2 F 2 newtons (N) 40r This is also the force on q2 due to the electric field of q : 1 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 2 r force distance qr 40r 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 = e 9E9(1.6021019 ) 10 14.4 volts 40r 1.010 and the electric field is: 19 e 9E9(1.60210 ) 10 2 20 14.410 volts/m 40r 1.010 14.4108 volts/cm 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 force 2 between two electrons, i.e., makes e true. F 2 -12 2 -1 -240r 0 8.854187817620... × 10 C ·N ·m 1 0 is the "magnetic constnant" called the 0 2 vacuum permeability 0c -7 -7 -2 -1 0 4 × 10 Henry/m 4 × 10 JA m 1 8.98755 109 9E9 c2 107 40 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. emission absorption 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 .