Find the magnetic field at $P$ due to the arrangement shown in the figure below.

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$\frac{μ_{0} i}{\sqrt{2} πd} (1 - \frac{1}{\sqrt{2}}) \otimes$

$\frac{2 μ_{0} i}{\sqrt{2} πd} \otimes$

$\frac{μ_{0} i}{\sqrt{2} πd} (1 + \frac{1}{\sqrt{2}}) \otimes$

$\frac{μ_{0} i}{\sqrt{2} πd} \otimes$

answer is A.

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Detailed Solution

$B = 2 [\frac{μ_{0}}{4 π} . \frac{i}{d \cos 45^{°}} \{\sin (- 45^{°}) + \sin 90^{°}\}] = \frac{μ_{0} i}{\sqrt{2} πd} [- \frac{1}{\sqrt{2}} + 1] . \otimes$

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