Question

In the given figure magnetic field at the centre of ring $\left(O\right)$ is $8\sqrt{2}T$. Now it is turned through a ${90}^o$ about $x{x}^{\prime }$ axis, so that two semicircular parts are mutually perpendicular. Then find the value of magnetic field (in Tesla) at centre.

Answer 1

Magnetic field of complete circle

$B=\frac{{\mu }_{0}I}{2R}$ or $8\sqrt{2}=\frac{{\mu }_{0}I}{2R}$

$\therefore \frac{{\mu }_{0}I}{R}=16\sqrt{2}$

now,

$B_1=B_2=\frac{{\mu }_{0}I}{4R}\sqrt{1^2+1^2}=\frac{\sqrt{2}}{4}\left(\frac{{\mu }_{0}I}{R}\right)$

$=\frac{1}{2\sqrt{2}}\ast 16\sqrt{2}=8T$