Problem 10.15A particle of charge q moves in a circle of radius a at constant angular velocity w. (Assume that the circle lies in the xy plane, centered at the origin, and at time 1 = 0 the charge is at (a, 0), on the positive x axis.) Find the Liénard-Wiechert potentials for points on the z axis.
Problem 10.15A particle of charge q moves in a circle of radius a at constant angular velocity w. (Assume that the circle lies in the xy plane, centered at the origin, and at time 1 = 0 the charge is at (a, 0), on the positive x axis.) Find the Liénard-Wiechert potentials for points on the z axis.
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Transcribed Image Text:II. PROBLEM 2. LIÉNARD-WIECHERT POTENTIALS.
Problem 10.15A particle of charge q moves in a circle of radius a at constant
angular velocity w. (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
Liénard-Wiechert potentials for points on the z axis.
It would be useful to parameterize the circle as
r(t) = a (cos (wt) + sin (wt)ÿ),
(1)
2
and then directly substitute the values into the Eqs. (10.46) and (10.47), i. e.
V (r, t) =
A(r,t) =V(r,t),
(2)
4TE0 2c - 4 v
where
|r – w (t,)|
2 =r - w (t,), t, =t -
=t -
(3)
and the velocity of the particle is also taken at the retarded time.
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