Many kinds of analysis in the physical sciences are helped by identifying quantities that are constant. It is usual to begin by assuming that the battery is ideal when analyzing these circuits l. Is any quantity (related to the battery) constant in circuits 7 & 8? If so, what quantity? (Hint; you should be able to use a DMM to measure it.)

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