Question

Find the magnetic field at P due to the arrangement shown

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

Answer 1

The correct option is A $\frac{{\mu }_{0}i}{\sqrt{2}\pi d}(1-\frac{1}{\sqrt{2}})\otimes$

$\begin{array}{c}B=\frac{\mu oi}{4\pi \left(d\cos {45}^0\right)}\left[\sin \left(-{45}^0\right)+\sin {90}^0\right]\\ =\frac{\sqrt{2}\mu oi}{4\pi d}\left[1-\frac{1}{\sqrt{2}}\right]2\\ =\frac{\mu oi}{\sqrt{2}\pi d}\left[1-\frac{1}{\sqrt{2}}\right]\end{array}$