The current in the wire is I. The current comes from infinite parallel to z-axis and finally goes to infinite parallel to y-axis as shown in the figure. Find magnetic field at O in vector form for the following current configurations.

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$\frac{μ_{0} . I}{4 πR} [\hat{j} + \frac{(2 + 7 π)}{4} (\hat{k})]$

$\frac{μ_{0} . I}{4 πR} [\hat{j} + \frac{(2 + 7 π)}{4} (- \hat{k})]$

$\frac{μ_{0} . I}{2 πR} [\hat{j} - \frac{(2 + 7 π)}{4} (- \hat{k})]$

None of these

answer is C.

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Detailed Solution

$\begin{array}{l} \vec{B} = \frac{μ_{0} I}{4 πR} \hat{j} - \frac{μ_{0} I}{4 πR} \frac{3 π}{2} \hat{k} - \frac{μ_{0}}{4 π} (\frac{I}{2 R}) \frac{π}{2} \hat{k} \\ - \frac{μ_{0}}{4 π} \frac{I}{2 R} \hat{k} = \frac{μ_{0} I}{4 πR} [\hat{j} - \frac{(7 π + 2)}{4} \hat{k}] \end{array}$

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