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Q.
Evaluate the magnitude and direction of magnetic field at point $O$
Moving Charges and Magnetism
Solution:
Magnetic field, $B_{1}=\frac{\mu_{0} i}{2 a} \cdot \frac{3}{4}=\frac{\mu_{0} i}{2 a} \cdot \frac{3}{4}=\frac{3 \mu_{0} i}{8 a} \odot$
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,
$B _{ O }= B _{1}+\left( B _{2}+ B _{3}\right)=\frac{3 \mu_{0} i }{8 a }+\frac{\mu_{0} i }{2 \sqrt{2 b }}, \odot$
