SOLVED: The calculation of the magnetic moment of a current loop leads to the line integral ∮𝐫× d 𝐫(a) Integrate around the perimeter of a current loop (in the x y -plane) and show that the scalar magnitude of this line integral is twice the area of the enclosed surface.(b) The perimeter of an ellipse is described by 𝐫=𝐱̂ a cosθ 𝐲̂ b sinθ. Frompart (a) show that the area of the ellipse is π a b.

Line, Surface, and Volume Integrals