Exercises

01

Polar divergence

Suppose $\mathbf{F}=\frac{1}{r^n}(-y,x)$ are the Cartesian components for $\mathbf{F}$ with $n$ some integer. Write this vector field using polar coordinates, and compute $\nabla \cdot \mathbf{F}$ using the polar formula for divergence. Repeat the exercise with $\mathbf{F}=\frac{1}{r^n}(x,y)$.