Aconducting sphere of radius r carries positive charge q. calculate the amount of work that would be required to move a small positive test charge q0 slowly from r=5r to r=3r. assume that the presence of q0 has no effect on how the charge q is distributed over the sphere.

express your answer in terms of the electric constant ϵ0 and some or all of the variables q, q0, and r.

People with normal vision cannot focus their eyes underwater if they aren't wearing a face mask or goggles and there is water in contact with their eyes. in a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the refraction occurs at the cornea, whose vertex is 2.60 cm from the retina.with the simplified model of the eye, what corrective lens (specified by focal length as measured in air) would be needed to enable a person underwater to focus an infinitely distant object? (be careful-the focal length of a lens underwater is not the same as in air! assume that the corrective lens has a refractive index of 1.62 and that the lens is used in eyeglasses, not goggles, so there is water on both sides of the lens. assume that the eyeglasses are 2.05cm in front of the eye.)