Constant Charge Density - Electromagnetism and Optics - Exam, Exams of Electromagnetism and Electromagnetic Fields Theory

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110A Fall 2006 Midterm This is a closed book exam, but you are allowed to bring one page of new formulas (as well as your page from the last midterm). Write your answers on the test or on extra sheets or on a blue book. You can write your answer as a definite integral. All quantities, including limits of integration, must be well specified. Show your work. There are 6 problems, check that you have them all. #1) (20 pts total) Consider an infinitely long cylinder of radius "a" that has constant charge density inside equal to p,> 0. Suppose that a point-charge of magnitude q > 0 is placed a distance a/4 from the center of the cylinder. What is the E-field (magnitude and direction) at the point "P" that is located a distance of a/2 from the center along a line that goes through the charge q (see picture)? = =) E baa Eyindi = Geo e \ 2 a aN \ B= (£2, «1 _)4 4&0 Weeat®