PHY 201 - Test 2

# PHY 201 - Test 2 - UNION COUNTY COLLEGE A semicircular disc...

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UNION COUNTY COLLEGE 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 σ =a*sin( θ ), where a is constant with units of coul/ m 2 , and θ is measured off the y-axis. Assume the potential is zero at infinity To find the potential "P we will break the semicircular disc up into elemental charges dq. Because we assume V(r= ) = 0, the contribution to the potential of "dq" is : dV dq 4 π ε 0 s where "s" is the disatnce from the charge element to the point in at which the potential is to be determined I n our case ; dq σ da σ a sin θ ( 29 Area Element in Polar Coordinates In the plane of the disk we chose polar components to use as our coordiante system, r =radial distance fron center and θ , the angle off of the y-axis da r dr d θ therefor dq a cos

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## This note was uploaded on 02/07/2011 for the course PHY 201 taught by Professor Gilbert during the Spring '11 term at Union County.

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PHY 201 - Test 2 - UNION COUNTY COLLEGE A semicircular disc...

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