P30_016 - that line are functions of y Replacing r with p y...

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16. Our y axis is along the wire with the origin at the top endpoint, and the current is in the positive y direction. All segments of the wire produce magnetic Felds at P that are into the page. According to the Biot-Savart law, the magnitude of the Feld any (inFnitesimal) segment produces at P is given by dB = µ 0 i 4 π sin θ r 2 dy where θ (the angle between the segment and a line drawn from the segment to P )and r (the length of
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Unformatted text preview: that line) are functions of y . Replacing r with p y 2 + a 2 and sin θ with a/r = a/ p y 2 + a 2 , we integrate from y = − a to y = 0. The total Feld is B = µ ia 4 π Z − a dy ( y 2 + a 2 ) 3 / 2 = µ ia 4 π 1 a 2 y ( y 2 + a 2 ) 1 / 2 ¯ ¯ ¯ ¯ ¯ − a = µ i 4 πa a √ a 2 + a 2 which simpliFes to the desired result (noting that 1 4 √ 2 = √ 2 8 )....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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