Question

Find the magnetic field $\overrightarrow{B}$ at the point P in figure.

Answer 1

Magnetic field at P due to SM and OQ is zero.Due to QR and RS are equal and outwards.Due to MN and NO are equal and inwards.
Due to QR and RS:
$B_1=2[\frac{{\mu }_o}{4\pi }\frac{I}{2a}(sin{0}^o+sin{45}^o)]$

$=-\frac{{\mu }_{o}I}{4\sqrt{2}\pi a}$ (outwards)

Due to MN and NO:
$B_2=2[\frac{{\mu }_o}{4\pi }\frac{I}{a}(sin{0}^o+sin{45}^o)]$

$=-\frac{{\mu }_{o}I}{2\sqrt{2}\pi a}$ (inwards)

$\therefore B_{net}=B_2-B_1=\frac{{\mu }_{o}i}{4\sqrt{2}\pi a}$ (inwards)