Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. the density of a neutron star is roughly 1014 times as great as that of ordinary solid matter. suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. the star's initial radius was 7.0×105km (comparable to our sun); its final radius is 15 km.

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