Since we just argued thatBis a constant at constant radius, we can pull it out of the integral alltogether.|B|Ids=μ0i⇒|B|=μ0i2πrwhich is exactly the equation we derived from the Biot-Savart law.10.4ProblemsProblem 29.24A current is set up in a wire loop consisting of a semicircle of radius 4cm, a smaller concentricsemicircle, 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 centerof curvature is 47.25μT. The smaller semicircle is then flipped over (rotated) until the loop isagain entirely in the same plane. The magnetic field produced at the (same) center of curvaturehow has magnitude 15.75μT, and its direction is reversed. What is the radius of the smallersemicircle?Figure 30: Figure for problem 29.24We first need to recognize that the straight portions of wire do not contribute to the magneticfield. We can see this from the Biot-Savart law becaused~sand~r
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