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PHY 201 - Test 2 - PHY 201 104 Test 2s UNION COUNTY COLLEGE...

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PHY 201 Test 2s UNION COUNTY COLLEGE 104 A semicircular disc of radius “R” carries a charge “Q” distributed non-uniformly over its surface. It is centered at the origin of the x-y-z coordinate system shown in the picture. The disc lies in the y- x plane The surface charge density is given by =a*sin( ), where a is constant with units of coul/m 2 , and is measured off the y-axis. Assume the potential is zero at infinity 1. Determine the constant “a’ in terms of “Q” and “R” We are asked to express the constant "a' in terms of "Q" and "R" I n our case ; dq da a sin   In the plane of the disk we chose polar components to use as our coordiante system, r =radial distance fron center and , the angle off of the y-axis Area Element in Polar Coordinates da r dr d therefor dq a sin   r dr d Q a d 0 R 0 a sin   d d Q a R 2 a Q R 2
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