Paper 3, Section II, B

Vector Calculus | Part IA, 2009

Give a necessary condition for a given vector field J\mathbf{J} to be the curl of another vector field B\mathbf{B}. Is the vector field B\mathbf{B} unique? If not, explain why not.

State Stokes' theorem and use it to evaluate the area integral

S(y2,z2,x2)dA\int_{S}\left(y^{2}, z^{2}, x^{2}\right) \cdot \mathbf{d} \mathbf{A}

where SS is the half of the ellipsoid


that lies in z0z \geqslant 0, and the area element dA points out of the ellipsoid.

Typos? Please submit corrections to this page on GitHub.