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Consider the situation as shown in figure. The magnitude of magnetic field at origin is

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$\frac{μ_{0} I \sqrt{π^{2} + 1}}{16 π^{2} r}$

$\frac{μ_{0} I \sqrt{π^{2} + 4}}{16 π^{2} r}$

$\frac{μ_{0} I \sqrt{π^{2} + 2}}{8 π^{2} r}$

$\frac{μ_{0} I \sqrt{π^{2} + 4}}{8 π r}$

answer is D.

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Detailed Solution

Question Image
${\vec{B}}_{1} = - \frac{μ_{0} I}{4 π r} \hat{i}$

${\vec{B}}_{2} = \frac{μ_{0} I}{8 r} \hat{k}$

${\vec{B}}_{0} = {\vec{B}}_{1} + {\vec{B}}_{2} = - \frac{μ_{0} I}{4 π r} \hat{i} - \frac{μ_{0} I}{8 r} \hat{k}$
$B_{0} = \frac{μ_{0} I}{4 r} \sqrt{\frac{1}{π^{2}} + {(\frac{1}{2})}^{2}} = \frac{μ_{0} I \sqrt{π^{2} + 4}}{8 π r}$

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