Question

Find the magnetic field at $P$ due to the arrangement shown

• A. $\frac{{\mu }_{0}i}{\sqrt{2}\pi d}\left(1-\frac{1}{\sqrt{2}}\right)\otimes$
• B. $\frac{2{\mu }_{0}i}{\sqrt{2}\pi d}\otimes$
• C. $\frac{{\mu }_{0}i}{\sqrt{2}\pi d}\otimes$
• D. $\frac{{\mu }_{0}i}{\sqrt{2}\pi d}\left(1+\frac{1}{\sqrt{2}}\right)\otimes$

Answer 1

Answer: (A)

$B=2\left[\frac{{\mu }_0}{4\pi },\frac{i}{d\cos 45^{\circ }}\left\{\sin \left(-45^{\circ }\right)+\sin 90^{\circ }\right\}\right]$
$\frac{{\mu }_{0}i}{\sqrt{2}\pi d}\left[-\frac{1}{\sqrt{2}}+1\right].\otimes$