EM equations + more Flashcards
What are Maxwell’s equations?
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What is the lorentz transformation of acceleration in the bremsstrahlung and synchrotron schema?
bremsstrahlung: gamma^3 factor
synchrotron: gamma^2 factor
(which is rest frame? (i think primed frame))
What are the equations for the electric and magnetic fields in terms of their potentials?
E is -(grad V) - time derivative of A
B is curl of A
What is the lorentz gauge condition for the electric and magnetic potentials?
1/c^2 (time derivative of V) + div(A) = 0
What are the wave equations for the electric and magnetic potentials?
wave operator on V gives rho/ epsilon0
wave operator on A gives mu0 * current density
wave operator= 1/c^2 second time derivative - laplacian operator
What is the lorentz force law?
force = charge * (E + v cross B)
What is the continuity equation for charge?
Divergence of current density + time derivative of charge density = 0
What is the equation for the Poynting vector?
1/mu0 * (E cross B)
What is the equation for EM energy density?
u = (e0 / 2) lEl^2 + (1/2*mu0) lBl^2
What are the electric and magnetic potential dipole terms?
electric: 1/(4 pi e0 r^2) * (electric dipole moment) dot (r-vector)
magnetic: mu0/(4 pi r^2) * (magnetic dipole moment) cross (r-vector)
What is the 4-differential?
Remember contravariant differential is differentiating with respect to the covariant 4-position and vice-versa.
contravariant 4-differential = (1/c time derivative, del)
What are the terms in the 4-momentum?
contravariant 4-momentum =
(E/c , 3-momentum)
= (gamma m c, gamma m 3-velocity)
What is the magnitude of the 4-momentum?
m^2 c^2
What is the relativistic kinetic energy of a particle?
(gamma - 1) m c^2
What are two forms of the relativistic energy of a particle?
E = gamma m c^2
E^2 = (pc)^2 + (mc^2)^2
What are the components of the 4-current?
charge density * 4-velocity
{4-velocity = (gamma * c, gamma * 3-velocity)}
What are the components of the 4-potential?
contravariant: (V/c , A)
What is the 4-wave operator?
What is the 4-wave equation?
4-wave operator: contravariant and covariant 4-derivatives
4-wave equation: 4-wave operator acting on the 4-potential = mu0 * the 4-current