Electromagnetism - EM Radiation

A charged particle, A, moving at a speed much less than c, decelerates uniformly. A second particle, B, has one-half the mass, twice the charge, three times the velocity, and four times the acceleration of particle A. According to classical electrodynamics, the ratio P_B/P_A of the powers radiated is

A. 16
B. 32
C. 48
D. 64
E. 72

(GR9677 #70)

Solution:

Larmor formula:
Power radiated by an accelerating non-relativistic point charge particle,
P = q²a² ⁄ 6πɛ₀c³

P does not depend on m and v.

P_B/P_A =  (2q)² (4a)² ⁄q²a²  =  64

Answer: D

Special Relativity - Momentum

A monoenergetic beam consists of unstable particles with total energies 100 times their rest energy. If the particles have rest mass m, their momentum is most nearly 

A. mc
B. 10 mc
C. 70 mc
D. 100 mc
E. 10⁴ mc

(GR9277 #70)

Solution:

E = γE₀ = 100E₀ → γ = 100
p = γm₀c = 100 mc

Answer: D

Special Relativity - Length Contraction

Questions 69-71

A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.

The length of the garage in the car’s rest frame is

A. 2.4 m
B. 4.0 m
C. 5.0 m
D. 8.3 m
E. Not determinable from the data given

(GR8677 #70)

Solution:

Length contraction: L = L₀/γ

Given for the garage, L₀ = 4 m
From problem GR8677 #69 → γ = 5/3

L = 4/(5/3) = 12/5 = 2.4 m

Answer: A

Optics - Interference

Light from a laser falls on a pair of very narrow slits separated by 0.5 micrometer, and bright fringes separated by 1.0 millimeter are observed on a distant screen. If the frequency of the laser light is doubled, what will be the separation of bright fringes?

A. 0.25 mm
B. 0.5 mm
C. 1.0 mm
D. 2.0 mm
E. 2.5 mm

(GR0177 #70)

Solution:

Double-slit interference:  

with


 

Answer: B