Homework 2
Due in class, Friday October 16

1. Field of a charged ring. A ring shaped conductor with radius a carries a total charge Q uniformly distributed around it, see figure. Find the electric field at a point, P, that lies on the axis of the ring at a distance x from its center. Show that for , the magnitude of the field increases linearly with x and that for , the field is the same as that of a point charge Q located at the center of the ring. Sketch the magnitude of the electric field as a function of x.

   

2. Field of a uniformly charged sphere. Positive electric charge Q is uniformly distributed throughout the volume of an insulating sphere of radius R. What is the direction of the electric field? Find the magnitude of the electric field at a point P a distance r from the center, both for r < R and r > R. Show that for r > R, the field is the same as if all the charge were concentrated at the center of the sphere.
   Hint: Use Gauss' theorem.

Young and Freedman

22-46, 22-52

Q23-2

23-5, 23-6, 23-15, 23-28, 23-44

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