5.1 Potential of a Moving Charge Flashcards
What is the Faraday tensor and Poynting vector proportional to for a moving charge with constant velocity
Faraday tensor is 1/r^2
N is 1/r^4
How much energy is radiated by a uniform moving charge?
0
What is the Faraday tensor and Poynting vector proportional to for an accelerating charge
Faraday tensor is 1/r
N is 1/r^2
How much energy is radiated by a accelerating moving charge?
A finite amount as it is proportional to r^0
Define is R_s?
Source observer distance measured at the retarded time in the source FoR
What is R_s equal to?
| = X^mu U_beta / c
r - r twiddle |
How is the electric field changed by γ?
Reduced by a factor of 1/γ^2
E = E_non rel * 1/γ^2
Describe how the electric field for a proton looks like for a relativistic and non relativistic case
Non-rel = normal uniform outward arrows. Isotropic
Rel - Elongated vertically, reduced horizontally. Anisotropic like the horizontally squished non relativistic one
Describe the power distribution for a relativistic and non relativistic case
Non-rel = Uniform circle rel = vertical mushroom cloud type shape
How are the 4 velocity and 4 acceleration related to each other?
Always orthogonal
- Like circular motion with v perp to a
What is the 4 velocity equal to?
U^mu = γ (c, v)
What is synchrotron radiation?
Highly relativistic radiation from an accelerated charge with v perp. a
- Circular motion with radiation emitted in a cone at a tangent
How can synchrotron radiation be created in a circle?
Using bending magnets
- Radiation beams go around in a circle with periodic bending magnets
What is a wiggler?
A set of alternating magnetic fields which wiggle a charge up and down
- Get flashes of intense x-rays
- Amplified n times for n magnet elements
What is an undulator
Coherent emission - monochromatic beam
- Phase match from each acceleration
What conditions can you use a wiggler and an undulator?
When the angle of the bending path is:
- Wiggler:»_space; than the change in angle of the cone of emission
- Undulator: «_space;than the change in angle of the cone of the emission
What is the four wavevector equal to?
(w/c , k)
What is synchrotron radiation useful for?
The wavelength is on the same order of magnitude of atomic separations
- Investigate the structure of materials
What is the four wavevector equal to?
(w/c , k)
What is synchrotron radiation useful for?
The wavelength is on the same order of magnitude of atomic separations
- Investigate the structure of materials
