Question

Evaluate the magnitude and direction of magnetic field at point $O$

• A. $\frac{3{\mu }_{0}i}{8a},\odot$
• B. $\frac{{\mu }_{0}i}{2\sqrt{2}b},\odot$
• C. $\frac{3{\mu }_{0}i}{8a}+\frac{{\mu }_{0}i}{2\sqrt{2}b},\odot$
• D. $\frac{3{\mu }_{0}i}{a}+\frac{{\mu }_{0}i}{2\sqrt{2}b},\otimes$

Answer 1

Answer: (C)

Magnetic field, $B_1=\frac{{\mu }_{0}i}{2a}\cdot \frac{3}{4}=\frac{{\mu }_{0}i}{2a}\cdot \frac{3}{4}=\frac{3{\mu }_{0}i}{8a}\odot$
Magnetic field, $B_2=\frac{{\mu }_{0}i}{4\pi b}\left(\cos 90^{\circ }+\cos 45^{\circ }\right)$
$=\frac{{\mu }_{0}i}{4\sqrt{2}\pi b}=B_3\odot$
Magnetic field at the centre O,
$B_O=B_1+\left(B_2+B_3\right)=\frac{3{\mu }_{0}i}{8a}+\frac{{\mu }_{0}i}{2\sqrt{2b}},\odot$