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Home , Coulomb constant, Electric field, Elementary charge, Impedance of free space, Permittivity, Vacuum permeability

564-17 Lec 34 Mon. 10Apr17 Tutorial on potentials, fields, and = ()=/ generated by a charge q in at a distance r in meters: q   J / C 40r

Where 0 = "the electric constant" or " " or "permittivity of free space" electric (volt/m) generated by a charge q at a distance r in meters: q   2 V / m 40r electrostatic of two charges at distance r apart: Coulomb's Law

q1q2 U  1q2  joules 40r

-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 ()

q1q2 F  2  newtons (N) 40r

This is also the force on q2 due to the 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 when a charge is moved a distance r in a constant electric field is given by:

q1q2 V  2 r force distance  qr 40r This is also the energy of a in a constant electric field: where qr = m = the dipole Some Reference Points For an , e the potential at 1 Å distance = e 9E9(1.6021019 )    10 14.4 40r 1.010 and the electric field is: 19 e 9E9(1.60210 ) 10   2  20 14.410 volts/m 40r 1.010 14.4108 volts/cm In proteins, electric fields on the order of 5 x 107 V/cm are common, and can shift emission by 50 nm. What exactly is the "electric constant", 0 ???, sometimes called the .

It is that number which gives the correct force 2 between two , i.e., makes e true. F  2 -12 2 -1 -240r  0  8.854187817620... × 10 C ·N ·m 1    0 is the "magnetic constnant" called the 0 2 0c -7 -7 -2 -1 0  4 × 10 /m  4 × 10 JA m 1  8.98755 109  9E9  c2 107 40

This nice number is also known as ke , the The constant 

•e is the elementary charge; •π is the irrational number ; •ħ = h/2π is the reduced ; •c is the 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 . 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 electrodynamics (QED), referred to the fine-structure constant in these terms: There is a most profound and beautiful question associated with the observed , e – the for a real to emit or absorb a real . 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 : 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 . 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