Why are "classical atoms" unstable?
Consider the current loop of width a and length b shown in the figure.
Find an expression for the vector potential that is valid anywhere.
A non-relativistic positron of charge qe and velocity v1 (v1 << c) impinges head-on on a fixed nucleus of charge Zqe. The positron which is coming from far away (∞), is decelerated until it comes to rest and then accelerated again in the opposite direction until it reaches a terminal velocity v2. Taking radiation loss into account (but assuming it is small), find v2 as a function of v1 and Z.
Let E0 = E0 k. The Abraham-Lorentz
force equation for a damped, charged, oscillator driven by an electric field
E0exp(-iωt) in the dipole approximation is
d2r'/dt2
+ Γ dr'/dt - τ d3r'/dt3 + ω02
r' = (q/m)E0exp(-iωt),
where Γ, τ, and ω0
are constants, q is the charge and m is the mass of the oscillator.
Using
this and the expression for the radiation electric field,
Erad(r,t)
= -(4πε0)-1[(q/(c2r'')]a⊥(t -
r''/c),
where r'' = r - r'(t - |r
- r'|/c),
show that the differential cross section for scattering of radiation of
frequency ω and polarization n = (θ/θ)
is
dσ/dΩ = (e2/(mc2))2
(k∙n)2[ω4/((ω02
- ω2)2 + ω2Γt2)],
where e2 = q2/(4πε0) and Γt = Γ
+ ω2τ.
A long thin cylinder carries a fixed uniform magnetization M parallel to its axis. Find the density, location and direction of the bound currents and the magnetic field at the geometrical center of the cylinder.