Introduction to Electrodynamics · Problem 1.19

Vector Analysis — David J. Griffiths

Physics · curl

Problem

Draw a circle in the

xy

plane. At a few representative points draw the vector

\mathbf{v}

tangent to the circle, pointing in the clockwise direction. By comparing adjacent vectors, determine the *sign* of

\partial v_x/\partial y

and

\partial v_y/\partial x

. According to Eq. 1.41, then, what is the direction of

\nabla \times \mathbf{v}

? Explain how this example illustrates the geometrical interpretation of the curl.