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CourseNotes.39

# CourseNotes.39 - Since we just argued that B is a constant...

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Since we just argued that B is a constant at constant radius, we can pull it out of the integral all together. | B | I ds = μ 0 i | B | = μ 0 i 2 πr which is exactly the equation we derived from the Biot-Savart law. 10.4 Problems Problem 29.24 A current is set up in a wire loop consisting of a semicircle of radius 4 cm , a smaller concentric semicircle, and two radial straight lengths, all in the same plane. Figure 30 shows the arrange- ment but is not drawn to scale. The magnitude of the magnetic field produced at the center of curvature is 47 . 25 μT . The smaller semicircle is then flipped over (rotated) until the loop is again entirely in the same plane. The magnetic field produced at the (same) center of curvature how has magnitude 15 . 75 μT , and its direction is reversed. What is the radius of the smaller semicircle? Figure 30: Figure for problem 29.24 We first need to recognize that the straight portions of wire do not contribute to the magnetic field. We can see this from the Biot-Savart law because d~s and ~ r
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