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Example: Find the magnetic field due to wire A'ACC' at O, which is the center of a circular arc carrying current i. Given are: i, R and 0.

Example: Find the magnetic field due to wire A'ACC' at O, which is the center of a circular arc carrying current i. Given are: i, R and 0.

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in this completed example, why is r equal to sintheta? Also the integration is dtheta, how do we get there? 

Example: Find the magnetic field due to wire A'ACC' at O, which is the center of a circular arc carrying current i. Given are: i, R and 0. For the arc segment AC: The magnetic field due to segments AA' and CC' is zero because ds xf = (ds) (sin0) = 0 where is in radians! B = Moi 4πR² dB = dB = So B ds = Mo i ds x f 4π r2 - Ho i ds sin90 4π R² Moi 4πR² Ꮎ Soº For a circular wire, 0 = 2π, and the magnetic field at the center of the loop is: μοί μοί 4πR 2R (2π) Rd0 = = Hoi 4πR Ꮎ . R C i C'
Transcribed Image Text:Example: Find the magnetic field due to wire A'ACC' at O, which is the center of a circular arc carrying current i. Given are: i, R and 0. For the arc segment AC: The magnetic field due to segments AA' and CC' is zero because ds xf = (ds) (sin0) = 0 where is in radians! B = Moi 4πR² dB = dB = So B ds = Mo i ds x f 4π r2 - Ho i ds sin90 4π R² Moi 4πR² Ꮎ Soº For a circular wire, 0 = 2π, and the magnetic field at the center of the loop is: μοί μοί 4πR 2R (2π) Rd0 = = Hoi 4πR Ꮎ . R C i C'
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