PHYS
• Example of Biot and Savart Law

• Example of Biot and Savart Law - Physics 202 Thursday...

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Physics 202 Thursday, April 1, 1999 Announcements: Lecture notes: Example of Biot and Savart Law Find the electric field due to current in a straight wire of infinite length What is B at point P? o Take point O to be the orgin. The positive z axis is out of the screen. o i ds and r are on the x -y plane. dB is in the +z direction. o dB = ( μ o /4 π )( i ds(cross)r / r 2 ) o Absolute value of dB = ( μ o /4 π )( i ds / r 2 )sin θ We now need to express the "sum" of the absolute value of dB in terms of a and θ 1 and θ 2 . o absolute value of ds = dx o x = a cot (180 - θ ) = - a cot θ . o dx = a csc 2 θ d θ . o r 2 = a 2 + x 2 = a 2 + a 2 cot 2 θ = a 2 ( 1+ cot 2 θ ) = a 2 csc 2 θ . o Therefore, Absolute value of dB = ( μ o /4 π )( i a csc 2 θ d θ sin θ / a 2 csc 2 θ ) o Simplified, Absolute value of dB = ( μ o /4 π )( i sin θ / a) d θ o B = ( μ o i/4 π a) I (integral from θ 1 to θ 2 ) sin θ d θ = -( μ o i/4 π a) cos θ (Evaluated from θ 1 to θ 2 )
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o B = ( μ o i/4 π a)(cos θ 1 - cos θ 2 ) If the wire is infinitely long, θ 1 goes to 0 and θ 2 goes to π
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