A current is set up in a wire loop consisting of a semicircle of radius 3.90 cm,

Question

A current is set up in a wire loop consisting of a semicircle of radius 3.90 cm, a smaller, concentric semicircle, and two radial straight lengths, all in the same plane. Figure (a) shows the arrangement but is not drawn to scale. The magnitude of the magnetic field produced at the center of curvature is 46.50 µT. The smaller semicircle is then flipped over (rotated) until the loop is again entirely in the same plane seen in Figure (b). The magnetic field produced at the (same) center of curvature now has the magnitude of 16.50 µT, and its direction is now reversed. What is the radius of the smaller semicircle?

Explanation / Answer

Suppose current in the semi circle is flowing counter-clockwise in (a) Now suppose that you superimpose a circular loop (radius r) of current flowing clockwise over the small semi circle in diagram (a) Then the net magnetic field would be that of that in (b) Since B = u I / (2 r) for a loop of current of radius r B = 46.5 - 16.5 = 30 * 10E-6 T r = u I / (2 B) where B is the change in the magnetic field due to the small loop. Let B1 be the original magnetic field B1 = u I / (4 R) + u I / (4 r) the field due to 2 semi circles B2 = u I / (4 R) - u I / (4 r) in configuration (b) B1 + B2 = u I / (2 R) adding equations Solve for I and substitute in the first equation to get r

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