I'm here today. 1. True 2. False

$\mathbf{A}(\mathbf{r}) = \dfrac{\mu_0}{4 \pi} \int \dfrac{\mathbf{J}(\mathbf{r}')}{\mathfrak{R}}d\tau'$ * By direct integration, find the vector potential at a distance $s$ from an finite straight wire carrying a current $I$ *Put the wire on the $z$-axis, from $z_1$ to $z_2$.* * In which direction does $\mathbf{A}$ point? Does that make sense to you? Why? * Check that $\nabla \cdot \mathbf{A} = 0$. * Check that $\nabla \times \mathbf{A} = \mathbf{B}$. * Is there an analogical problem that we can use to find $\mathbf{A}$, that is, instead of using direct integration?

Consider the many magnetic field problems that you have solved. Using a previously solved problem where you know the current density and magnetic field, develop a physical situation where the structure of the solved problem for $\mathbf{B}$ matches one for an unsolved problem for $\mathbf{A}$. You are trying to build the analogy between two different problems whose mathematical structure is similar (like we did for the solenoid and the thick wire). Recall, $\nabla \times \mathbf{B} = \mu_0 \mathbf{J}$ $\nabla \times \mathbf{A} = \mathbf{B}$

For your unsolved problem, what is $\mathbf{B}$? What current density, $\mathbf{J}$ gives rise to your unsolved problem?