1. Astronomical observatories have been available since ancient times, and many cultures set aside special sites for astronomical observations. The thing modern observatories have that was missing from these older observatories until about 1610 was: a. a dark site, where lights did not get in the way b. graduate students or other assistants for sharing the astronomer’s work c. a method of keeping good records d. a way of measuring from what general direction in the sky a beam of light was coming e. telescopes

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