Electricity and Magnetism I (P331)Homework 2Due: Wednesday, September 16, 4:00 PM1. Find the magnitude of the electric field at a distancezabove a circular loop of chargeQand radiusa.Compute the electric field by directly integrating over the charge distribution14π0λ2dlˆ. (Here, ˆ isthe separation vector, “scriptr” in the text.)2. The electric field in some region of space is given byE=α(r4-1r)ˆrin spherical coordinates.(a) Find the charge densityρ.(b) Use your answer to (a) to find the total charge contained in a sphere of radiusRcentered at theorigin.(c) Check your answer to (b) by using the integral form of Gauss’ Law to find the total charge containedin a sphere of radiusRcentered at the origin.3. Assume there is a ribbon of electric charge in thex, yplane. It extends from-a≤y≤ain theydirection and infinitely long in thexdirection. If the surface charge density isσ, calculate the electricfield at the position (0,0, d). (A distancedabove the origin on thezaxis.)
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