Electromagnetism – Gauss' Law

A uniformly charged sphere of total charge Q expands and contract between radii R₁ and R₂  at a frequency f. The total power radiated by the sphere is

A. proportional to Q
B. proportional to f²
C. proportional to f⁴
D. proportional to (R₁ / R₂)
E. zero

(GR0177 #96)

Solution:

Power, P = VI
I = dq / dt
Q is constant → dq = 0 → I = 0  → P = 0

Answer: E

Optics – Michelson Interferometer

A gas-filled cell of length 5 cm is inserted in one arm of a Michelson interferometer as shown in the figure. The interferometer is illuminated by light of wavelength 500 nanometers. As the gas is evacuated from the cell, 40 fringes cross a point in the field of view. The refractive index of this gas is most nearly?

A. 1.02
B. 1.002
C. 1.0002
D. 1.00002
E. 0.98

(GR9277 #96)

Solution:

Michelson interferometer, 2ΔL = Nλ
N = ^2ΔL/_λ

N_vac = ^2ΔL/_λvac
N_gas = ^2ΔL/_λgas

λ_gas = ^λ_vac/_n
N_gas = ^2ΔL/_λgas  = ^2ΔLn/_λvac

ΔN = N_gas − N_vac
= ^2ΔLn/_λvac − ^2ΔLn/_λvac
= ^2ΔL/_λvac (n − 1)

Given:
ΔL = 5 cm = 5 × 10⁻² m
ΔN = 40 fringes
λ_vac = 500 nm  = 5 × 10⁻⁷ m

40 = [2(5 × 10⁻²)/(5 × 10⁻⁷)](n − 1)
40 = (2 × 10⁵)(n − 1)
40/(2 × 10⁵) = n − 1
2 × 10⁻⁴ = n − 1
n = 0.0002 + 1 = 1.0002

Answer: C

Nuclear & Particle Physics – Conservation Laws

Which of the following reasons explains why a photon cannot decay to an electron and a positron γ → e⁻ + e⁺ in free space?

A. Linear momentum and energy are not both conserved
B. Linear momentum and angular momentum are not both conserved
C. Angular momentum and parity are not both conserved
D. Parity and strangeness are not both conserved
E. Charge and lepton number are not both conserved

(GR9677 #96)

Solution:

See GR0177 #99

Answer: A