(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I had several questions about the magnetic field vector.

For example when applying the Biot-Savart Law, I was under the impression that each differential element [itex]{d{\vec{s}}}[/itex] containing a current [itex]{I}[/itex] along an infinitely long straight wire exerts a magnetic field according to the right-hand-rule (R.H.R.), [itex]{\vec{B}}[/itex] around and perpendicular to that differential segement [itex]{d{\vec{s}}}[/itex]. As shown below,

However, I then came across this figure which more clearly shows that--from a differential segement [itex]{d{\vec{s}}}[/itex] with a current [itex]{I}[/itex] at a distance [itex]{\vec{r}}[/itex] oriented at an angle from [itex]{d{\vec{s}}}[/itex] there is a differential magnetic field [itex]{d{\vec{B}}}[/itex] due to this segment. As shown below,

2. Relevant equations

Biot-Savart Law

[tex]

{d{\vec{B}}} = {{\frac{{\mu}_{0}}{4{\pi}}}{\cdot}{\frac{Id{\vec{s}}{\times}{\vec{r}}}{{r}^{3}}}}

[/tex]

3. The attempt at a solution

This is a little confusing as I assumed that from the R.H.R. visualization of a magnetic field due to a current; that it showed that the magnetic field goes around the current at that particular segment (like a ring) and is oriented perpendicular to the current at that particular length segment.

So, then how is the magnetic field really supposed to be visualized if the R.H.R. visualization suggests it is exerted like a ring around a particular segment of current? As opposed to the other visualization suggesting that the magnetic field from a particular segement is like a ring that goes all the way up and down along the current and always perpendicular to the current.

So, how is it that the magnetic field is supposed to be visualized?

Any help is appreciated.

Thanks,

-PFStudent

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# Homework Help: Biot-Savart Law & Magnetic Field: Clarification

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