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1. Homework Statement

1. Homework Statement

One must simply calculate the magnetic field at a distance

**to the wire, which carries a steady current [tex]I[/tex]**

*s*## Homework Equations

Should I write the point vector as:

[tex]\mathbf{r} = s\hat{s} + \phi \hat{\phi} + z \hat{z}[/tex]

or

[tex]\mathbf{r} = s\hat{s} + z \hat{z}[/tex] ?

## The Attempt at a Solution

I am not solving it as the author does. I am trying to use spherical coordinates, therefore I am writing:

[tex]\mathbf{B}(\mathbf{r}) = \frac{\mu_0}{4\pi}\int_{-\infty}^\infty{\frac{d\mathbf{l'} \times (\mathbf{r} - \mathbf{r'})}{|(\mathbf{r} - \mathbf{r'})|^{3/2}}}[/tex]

[tex] [/tex]

Where:

[tex]d\mathbf{l'} = dz \hat{z} [/tex]

[tex]\mathbf{r} - \mathbf{r'} = s \hat{s} + z \hat{z} - z'\hat{z} = s \hat{s} + (z-z')\hat{z}[/tex]

and the answer is fine:

[tex]\mathbf{B}(\mathbf{r}) = \frac{\mu_0}{4\pi} \frac{2 I}{s} \hat{\phi}[/tex]

But, if I consider the vector as:

[tex]\mathbf{r} = s\hat{s} + \phi \hat{\phi} + z \hat{z}[/tex]

(it seems to me more general) The answer has a component in the s-direction, which is incorrect.

Please, what is wrong in my reasoning?