Suppose that you want to test the effects of different dishwashing detergents on dishes that have food stuck to them. to test the differences, you wa sh three loads of the same dishes, each with a different type of detergent, a ll in warm water. you also wash a fourth load of dishes with only warm water. i dentify the control, dependent variable, and independent variable in the exper iment. explain your answer.

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