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enter image description here

In the answer section it is written that,The magnetic field at O due to the current in the straight segments $AA^\prime$ and $CC^\prime$ is zero because ds is parallel to along these paths.

My querry is that "How ds is parallel to along these paths?"

EDIT: enter image description here

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  • $\begingroup$ The magnetic field at "O" due to current in AA' and CC' is zero irrespective of ds - where did you get the quote? $\endgroup$
    – Andy aka
    Nov 3, 2013 at 17:35
  • $\begingroup$ Resnick Hallyday modern physics page no 941. Iam adding the screenshot. $\endgroup$
    – user2378
    Nov 3, 2013 at 17:52

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ds, as a segment of the wire carrying current, produces a magnetic field at "O" from all points that the wire is curved. When the wire is in the AA' section or the CC' section ds (as an arbitrarily small section of the wire) MUST now point at the origin and therefore it will not produce a magnetic field at the origin.

In your question you probably mistakingly omited the $\hat{r}$ part which is why I asked for clarification.

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  • $\begingroup$ But why ds is paral- lel to $\hat r$ $\endgroup$
    – user2378
    Nov 3, 2013 at 18:40
  • $\begingroup$ $\hat{r}$ is a vector produced by current and always points at O. When ds is on the section AA' or CC' $\hat{r}$ still points at O but it is now in parallel with ds. $\endgroup$
    – Andy aka
    Nov 3, 2013 at 18:46

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