- #1
Harry134
- 1
- 0
Hi,
Consider the vector potential, [itex]\vec{A}(\vec{x})[/itex], below. The problem is to calculate [itex]\vec{A}(\vec{x})[/itex] explictly, and show that it has components [itex]A_{r}[/itex], [itex]A_{\theta}[/itex] and [itex]A_{\phi}[/itex]
[itex]\vec{A}(\vec{x})[/itex] = [itex]\frac{g}{4\pi} \int_{-\infty}^{0} \frac{dz' \hat{z} \times (\vec{x} - z' \hat{z})}{\vert \vec{x} - z' \hat{z} \vert ^{3}}[/itex]
[itex]A_{r} = 0[/itex], [itex]A_{\theta} = 0[/itex], [itex]A_{\phi} = \frac{g}{4 \pi} \frac{\tan{\theta / 2}}{R}[/itex]
This is a homework problem and I have seen the solution to it. However, I do not understand any of the solution or even where to start the problem.
Thanks
Homework Statement
Consider the vector potential, [itex]\vec{A}(\vec{x})[/itex], below. The problem is to calculate [itex]\vec{A}(\vec{x})[/itex] explictly, and show that it has components [itex]A_{r}[/itex], [itex]A_{\theta}[/itex] and [itex]A_{\phi}[/itex]
Homework Equations
[itex]\vec{A}(\vec{x})[/itex] = [itex]\frac{g}{4\pi} \int_{-\infty}^{0} \frac{dz' \hat{z} \times (\vec{x} - z' \hat{z})}{\vert \vec{x} - z' \hat{z} \vert ^{3}}[/itex]
[itex]A_{r} = 0[/itex], [itex]A_{\theta} = 0[/itex], [itex]A_{\phi} = \frac{g}{4 \pi} \frac{\tan{\theta / 2}}{R}[/itex]
The Attempt at a Solution
This is a homework problem and I have seen the solution to it. However, I do not understand any of the solution or even where to start the problem.
Thanks