 ## Section 5.3  ELECTROMAGNETIC RELATIONS Gaussian CGS SI Units and conversions: Charge 2.997 92 ´ 109 esu = 1 C = 1 A s Potential (1/299.792) statvolt = (1/299.792) erg/esu = 1 V = 1 J C–1 Magnetic field 104 gauss = 104 dyne/esu = 1 T = 1 N A–1 m–1 Electron charge e = 4.803 204 ´ 10–10 esu = 1.602 176 ´ 10–19 C Lorentz force  Maxwell equations        Linear media  Permittivity of free space  Permeability of free space  Fields from potentials    Static potentials (coulomb gauge)    Relativistic transformations (v is the velocity of primed system as seen in un- primed system)           Impedances (SI units)

r = resistivity at room temperature in 10–8 W m:

~ 1.7 for Cu                         ~ 5.5 for W

~ 2.4 for Au                         ~ 73 for SS 304

~ 2.8 for Al                          ~ 100 for Nichrome

(Al alloys may have
double this value.)

For alternating currents, instantaneous current I, voltage V, angular frequency w: .

Impedance of self-inductance L:  Z = jwL .

Impedance of capacitance C:  Z = 1/jwC .

Impedance of free space: .

High-frequency surface impedance of a good conductor: , where d = effective skin depth ; for Cu .

Capacitance and inductance per unit length (SI units)

Flat rectangular plates of width w, separated by d << w with linear medium (e, m) between: ; = 2 to 6 for plastics; 4 to 8 for porcelain, glasses;  .

Transmission lines (no loss):

Impedance: .

Velocity: .

Motion of charged particles in a uniform, static magnetic field

The path of motion of a charged particle of momentum p is a helix of constant radius R and constant pitch angle l, with the axis of the helix along B: ,

where the charge q is in units of the electronic charge.  The angular velocity about the axis of the helix is ,

where E is the energy of the particle.

This section was adapted, with permission, from the 1999 web edition of the Review of Particle Physics (http://pdg. lbl.gov). See J. D. Jackson, Classical Electrodynamics, 2d ed. (John Wiley & Sons, New York, 1975) for more formulas and details. A PDF version of this table is also available.