Oscillating charge, larmor power dissipation

[unscientific]

Homework Statement

A z-polarized incident EM waves hits a small charge (-q) bounded to a massive charge (+q) with spring constant k0 and frequency ω.

(a) Write down the equation of motion

(b)Find time averaged total power dissipated.

(c) Find classical scattering cross section σ (thomson)

(d) Find value of E0 that makes magnetic forces non-negligible.

The Attempt at a Solution

Part (a) and (b)

Part(c)

Part (d)
Because velocity of particle is slow, so magnetic force on it is low, giving it a small magnetic displacement compared to the electric displacement.

I related equated magnetic displacement to electric displacement to find a value of E₀.

 

[unscientific]

I'm not sure if part (d) is right.

 

[unscientific]

bumpp

 

[unscientific]

bumpp

 

[TSny]

As far as I can tell:

(a) OK
(b) The mass occurring in the fraction part of your answer should be replace by some other quantity. Otherwise, OK.
(c) Fixing (b) will affect the answer for (c).
(d) OK

Note, you should make a dimensional analysis of your results. This would help you see that your answers for (b) and (c) can't be correct.

 

[unscientific]

As far as I can tell:

(a) OK
(b) The mass occurring in the fraction part of your answer should be replace by some other quantity. Otherwise, OK.
(c) Fixing (b) will affect the answer for (c).
(d) OK

Note, you should make a dimensional analysis of your results. This would help you see that your answers for (b) and (c) can't be correct.

I mistakenly thought p = momentum, but it should be p = qx, so the m² should be replaced by charge, q².

 

[TSny]

Right.