Problem set 01

Problem 1

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

$$I={\int }_{\mathcal{V}}d\mathbf{r}\exp (-\mu r)(\mathrm{\nabla }\cdot \frac{\hat{\mathbf{r}}}{r^2}).$$

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

Problem 2

An electrostatic potential has the expression $\varphi (r)=q\exp (-\mu r)/r$, 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