4321_HW3FA08 - Physics 4321 Homework Set 3 Due September 8...

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Physics 4321 Homework Set 3 September 8, 2008 Due: September 15, 2008 Recall that the units vectors parallel to x, y, and z are given by x ^ , y ^ , and z ^ , respectively. 1. (a) Calculate the electric field a distance z above the midpoint between two equal charges, q , a distance d apart. Check your result for z >> d . (b) Repeat the calculation when the charge at ( x = - d /2 is replaced with a negative charge - q . 2. (a) Calculate the electric field a distance z above the center of a square loop of side a , which carries a uniform line charge λ . (b) How would your results differ if each segment of the square loop had a different charge density? 3. A flat, circular disk in the xy plane carries a uniform charge density + σ from φ = 0 to 180 degrees and a uniform charge density - σ from 180 to 360 degrees. Calculate the electric field at a point r = z z ^ . Note: The x- axis lies along φ = 0 degrees. 4. The electric field in some region is given by E = kr 3 r ^ , where k is a constant. (a) Calculate the charge density ρ . (b) Calculate the total charge Q
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