Spaceship flies past mars with a speed of 0.985c rela- tive to the surface of the planet. when the spaceship is directly overhead, a signal light on the martian surface blinks on and then off. an observer on mars measures that the signal light was on for 75.0 ms. (a) does the observer on mars or the pilot on the space- ship measure the proper time?

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