A particle of charge q moves in a circle of radius α at constant angular velocity ω. (Assume that...

Question

A particle of charge q moves in a circle of radius α at constant angular velocity ω. (Assume that the circle lies in the xy plane, centered at the origin, and at time t = 0 the charge is at (a, 0), on the positive x axis.) Find the Lienard-Wiechert potentials for points on the z axis.

David · Accepted Answer

Solution 
The general forms of the Liénard-Wiechert potentials for a charge q are, 
qc 
V (ṙ, t)   = Eq. 10.39 (1) 
4πso(Rc − Ṙ  · ̇v) 
Ȧ(ṙ, t)   = 
  µoqcv̇
4π(Rc − Ṙ  · ̇v) 
= 
v̇  
V (ṙ, t) Eq. 10.40 (2) 
c2 
where my is equivalent to the lower case script r of Griffiths because making lower case 
script r’s appears to be beyond my ability. 
The particle is confined to move in a circle. Such a trajectory may be written as, 
ẇ(t) = a[cos(ωt) x̂ + sin(ωt) ŷ] (3) 
 
using the initial condition given in the problem. The location of the particle at the retarded 
time is found by replacing t with tr above. 
The vector from the source (i.e.

A particle of charge q moves in a circle of radius α at constant angular velocity ω. (Assume that the circle lies in the xy plane, centered at the origin, and at time t = 0 the charge is at (a, 0), on...

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