A wire carrying a current I is bent into the shape of an exponential spiral, r = eθ, from θ = 0 to θ = 2π 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 (θ) is related to the function in the following way: Thus in this case r = e θ, tan B = 1 and B = π/4. Therefore, the angle between ds and r is π - B = 3π/4. Also

Transcribed Image Text:

tan β dr/ do s case r.:εθ, tan β e angle between ds and f dr sin(/4)