Question

Calculate the magnetic field at the point O of a loop with current $i$ whose shape is as shown in the figure.

Answer 1

Magnetic field at the center due to a current carrying circular part is given by,

$B=\frac{{\mu }_{0}I\theta }{2\pi r}$

${\theta }_1=\frac{\pi }{2}$, ${\theta }_2=\frac{3\pi }{2}$

$r_1=a$, $r_2=b$

$\therefore B=\frac{{\mu }_{0}I{\theta }_1}{2\pi r_1}+\frac{{\mu }_{0}I{\theta }_2}{2\pi r_2}$

$=\frac{{\mu }_{0}I}{2\pi \times a\times 2}\times \pi +\frac{{\mu }_{0}I}{2\pi b}\times \frac{3\pi }{2}$

B$=\frac{{\mu }_{0}I}{4a}+\frac{3{\mu }_{0}I}{4b}$