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 0.800 c, 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

This is a length contraction problem, where the length of the rod is contracted as observed from Pluto due to the spaceship travelling at 0.800 c relative to Pluto. The formula for length contraction is L' = L/sqrt(1-v^2/c^2), where L is the original length, v is the relative velocity, c is the speed of light, and L' is the contracted length. Plugging in the values, we get L' = L₀/sqrt(1-0.800^2) = L₀/0.6. The linear charge density is defined as λ = Q/L, where Q is the charge and L is the length. Substituting L' for L, we get λ' = Q/L' = Q/L₀*0.6 = 1.67 λ₀. Therefore, the linear charge density observed from Pluto is 1.67 times the original linear charge density. The best choice is E, 1.67 λ₀.

In a Classroom on the First Spaceship to an Extrasolar