Problem set 01

Problem 1

Use the two methods methods introduced in Example 1.16 in the book to evaluate the integral

$$I = \int_{{\cal V}} d{\mathbf{r}} \exp{(-\mu r)} \left(\mathbf{\nabla} \cdot \frac{\hat{\mathbf{r}}}{r^2} \right).$$

${\cal V}$ is a sphere with radius $R$.

Problem 2

An electrostatic potential has the expression $\phi(r) = q \exp{(-\mu r)}/r$, where $q$ and $\mu$ are constants.

(a) Find the electric field.

(b) Find the charge distribution creating the potential.

(c) Find the total charge. Are we missing some charge?

Problem 3

Find curl and divergence of the vector field $\mathbf{F} = (\mathbf{r}\times\mathbf{p})(\mathbf{r}\cdot\mathbf{p})$, where $\mathbf{p}$ is a constant vector.

The problems are due Monday January 20 2025 at 20:00