(Solution) - A wire carrying a current I is bent -(2025 Original AI-Free Solution)

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A wire carrying a current I is bent into the shape of an exponential spiral, r = e?, from ? = 0 to ? = 2? as suggested in Figure P30.69. To complete a loop, the ends of the spiral are connected by a straight wire along the x axis. Find the magnitude and direction of B at the origin. Suggestions: Use the Biot?Savart law. The angle 9 between a radial line and its tangent line at any point on the curve r = f (?) is related to the function in the following way: Thus in this case r = e ?, tan B = 1 and B = ?/4. Therefore, the angle between ds and r is ? - B = 3?/4. Also