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RECITATION-CH30 - RECITATION 11 7 Each of the semi-infinite...

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RECITATION 11 7. Each of the semi-infinite straight wires contributes 0 4 i R μ π (Eq. 30-9) to the field at the center of the circle (both contributions pointing “out of the page”). The current in the arc contributes a term given by Eq. 30-11 pointing into the page, and this is able to produce zero total field at that location if arc straight 0 0 2 2 4 4 C B B i i R R μ φ μ π π = = which yields 2 rad 115 . C φ = ° 11. Our x axis is along the wire with the origin at the midpoint. The current flows in the positive x direction. All segments of the wire produce magnetic fields at P 1 that are out of the page. According to the Biot-Savart law, the magnitude of the field any (infinitesimal) segment produces at P 1 is given by 0 2 sin 4 i dB dx r μ φ π = where φ (the angle between the segment and a line drawn from the segment to P 1 ) and r (the length of that line) are functions of x . Replacing r with 2 2 x R + and sin φ with 2 2 , R r R x R = + we integrate from x = –L /2 to x = L /2. The total field has a magnitude of
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