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hw2 - Electricity and Magnetism I(P331 Homework 2 Due...

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Electricity and Magnetism I (P331) Homework 2 Due: Wednesday, September 16, 4:00 PM 1. Find the magnitude of the electric field at a distance z above a circular loop of charge Q and radius a . Compute the electric field by directly integrating over the charge distribution 1 4 π 0 λ 2 dl ˆ. (Here, ˆ is the separation vector, “script r ” in the text.) 2. The electric field in some region of space is given by E = α ( r 4 - 1 r r in spherical coordinates. (a) Find the charge density ρ . (b) Use your answer to (a) to find the total charge contained in a sphere of radius R centered at the origin. (c) Check your answer to (b) by using the integral form of Gauss’ Law to find the total charge contained in a sphere of radius R centered at the origin. 3. Assume there is a ribbon of electric charge in the x, y plane. It extends from - a y a in the y direction and infinitely long in the x direction. If the surface charge density is σ , calculate the electric field at the position (0 , 0 , d ). (A distance d above the origin on the z axis.)
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