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.

Arunner is jogging at a steady 3.6 km/hr. when the runner is 2.9 km from the finish line, a bird begins flying from the runner to the finish line at 14.4 km/hr (4 times as fast as the runner). when the bird reaches the finish line, it turns around and flies back to the runner. even though the bird is a dodo, we will assume that it occupies only one point in space, i.e., a zero-length bird. how far does the bird travel? (b) after this first encounter, the bird then turns around and flies from the runner back to the finish line, turns around again and flies back to the runner. the bird repeats the back and forth trips until the runner reaches the finish line. how far does the bird travel from the beginning? (i.e. include the distance traveled to the first encounter)