Electromagnetism - EM Radiation

An electron oscillates back and forth along the + and − x-axes, consequently emitting electromagnetic radiation. Which of the following statements concerning the radiation is NOT true?

1. The total rate of radiation of energy into all directions is proportional to the square of the electron's acceleration.
2. The total rate of radiation of energy into all directions is proportional to the square of the electron's charge.
3. Far from the electron, the rate at which radiated energy crosses a perpendicular unit area decreases as the inverse square of the distance from the electron
4. Far from the electron, the rate at which radiated energy crosses a perpendicular unit area is a maximum when the unit area is located on the + or − x-axes
5. Far from the electron, the radiated energy is carried equally by the transverse electric and the transverse magnetic fields.

(GR9277 #84)

Solution:

Power radiated, P = ∮ S ∙ dA
S is poynting vector, where S = (1/μ₀) E × B  = (1/cμ₀) |E|²
Electric field, E = − (kq/r)(a_⊥/c²)

(A) TRUE
P ∝ a²  since |E|² ∝  a_⊥²

(B) TRUE,
P ∝ q² since |E|² ∝ q²

(C) TRUE
P ∝ 1/r² since |E|² ∝ 1/r²

(D) FALSE
The electron oscillates back and forth along the + and − x-axes. Thus, the direction of acceleration is along the + and − x axes. P_max is when the area of electric flux perpendicular, ⊥ to the acceleration of the particle (not located on the + or − x-axes).
P_max ∝ a_⊥² since |E|² ∝  a_⊥²

(E) TRUE, 
Power radiated, P = ∮ S ∙ dA
S is poynting vector, where S = (1/μ₀) E × B
P is carried equally by E and B field.

Answer: D