In a classroom on the first spaceship to an extrasolar planet--there are children because the trip will take 200 years--a teacher is showing charge Q uniformly distributed along a conducting rod of length L0 to produce linear charge density λ₀. As observed on Pluto when the spaceship passes it at 0.800c, the linear charge density is A)0.360 λ₀. B)0.600 λ₀. C)0.800 λ₀. D)1.00 λ₀. E)1.67 λ₀.

Question

Quizplus · Accepted Answer

From the point of view of the observer on Pluto, the length of the rod will appear contracted due to length contraction. The contracted length, L, will be given by: L = L0/γ where γ = 1/√(1-v^2/c^2) is the Lorentz factor and v = 0.8c is the velocity of the spaceship relative to Pluto. The charge per unit length will remain the same in both frames, so we can use: λ = Q/L0 = Qγ/L The linear charge density observed on Pluto will be: λ' = λ/γ = (Q/L0)√(1-v^2/c^2) Substituting λ = Q/L0 and L = L0/γ, we find: λ' = Q/(L0γ)√(1-v^2/c^2) λ' = λ₀/√(1-v^2/c^2) λ' = λ₀/√(1-(0.8c/c)^2) λ' = 1.67λ₀ Therefore, the linear charge density observed on Pluto is 1.67 times the value observed in the rest frame of the spaceship, so the best answer is E.

In a Classroom on the First Spaceship to an Extrasolar