Physics
1. Visualizing Fields Say a strip of width a lies in the x-y-plane aligned with the x-axis. This sheet carries a uniform (postive) charge per unit area s > 0. The edges of this sheet are separate elements that each carries a uniform (negative) charge per unit length ? < 0. Assume the entire system has a net negative charge, and draw the electric ï¬eld lines that lie within a cross section through this system that includes the z-axis. Include enough detail to show all the salient features of the ï¬eld.
2. Practice Superposing Fields
(a) Find the electric ï¬eld inside and outside a uniformly charged spherical shell with surface charge density s and radius R by superposing the electric ï¬elds produced by a collection of charged rings (use expressions derived in Example 3.1).
(b) Find the electric ï¬eld everywhere along the axis of a uniformly charged cylinder with volume charge density ? radius R and length L by superposing the electric ï¬elds produced by a collection of charged disks (again, computed in Example 3.1). Verify that you get a sensible value for the electric ï¬eld in the middle of the cylinder.
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