Current $I$ is flowing in conductor shaped as shown in the figure. The radius of the curved part is $r$ and the length of straight portion is very large. The value of the magnetic field at the centre $O$ will be
Diffcult
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${{\text{B}}_{\text{A}}} = 0$
${{\text{B}}_{\text{B}}} = \frac{{{\mu _0}}}{{4\pi }}\frac{{(2\pi - \pi /2){\text{I}}}}{{\text{r}}} \otimes $
$ = \frac{{{\mu _0}}}{{4\pi }}\frac{{3\pi {\text{I}}}}{{2{\text{r}}}}$
$\mathrm{B}_{\mathrm{C}}=\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{r}} \otimes $
So, net magnetic field at the centre $=\mathrm{B}_{\mathrm{A}}+\mathrm{B}_{\mathrm{B}}+\mathrm{B}_{\mathrm{C}}$
$=0+\frac{\mu_{0}}{4 \pi} \frac{3 \pi \mathrm{I}}{2 \mathrm{r}}+\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{r}}=\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{r}}\left(\frac{3 \pi}{2}+1\right)$
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