A poor artist might approximate a flower as a series of radial lines and circular arcs. We could characterize the flower by specifying the inner and outer radii, and the inner and outer angles (shown). If a current I flows around along the lines and arcs as shown, a magnetic field may be generated at the center of the flower. For the figure as drawn, please answer each of the following questions.

What is the direction of the magnetic field?

Which produces a larger contribution to the field, the radial lines or the arcs?

Holding the other variables fixed, will increasing Router make the field bigger? Smaller? No effect?

Holding the other variables fixed, would making thetaouter bigger and thetainner smaller make the field bigger? Smaller? No effect?

Would increasing the number of "petals" make the field bigger? Smaller? No effect?