You are in a rocket moving away from Earth at one-third the speed of light relative to Earth. A friend is on Earth, and an astronaut in another rocket is moving toward Earth at one-third the speed of light (in the Earth reference frame), on a path collinear with your path.

If each of you records the duration of your journey in your three respective reference frames, which of you records the proper time interval?

Check all that apply.

a. Your friend records your proper time interval.
b. The astronaut records your proper time interval.
c. You record your own proper time interval.
d. Nobody records your proper time interval.

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants