Liénard-Wiechert Potential for Spiraling Charge
Liénard-Wiechert Potential for Spiraling Charge
The graphics show different views of the radiation patterns produced by a point charge moving in an inward spiral trajectory with angular velocity . Since a charge moving in a circular orbit is continually undergoing centripetal acceleration , it radiates away energy in accordance with Larmor's formula = (in Gaussian units). As energy is lost, the radius decreases as the charge spirals inward toward the attracting center. Neglecting any contribution from the radiation field, the Liénard–Wiechert scalar potential produced by the moving charge is computed. This treatment is valid for , and thus excludes the ultrarelativistic domain.
ω
a=/r=r
2
v
2
ω
E
t
2
2
e
2
a
3
3
c
Φ(r,t)
v≪c