Answer to Question #135011 in Optics for Afraid

Question

Two current-carrying circular loops, each of radius R , are placed
perpendicular to each other, as shown in the figure.
The loop in the xy - plane carries a current I_0while that in the
xz -plane carries a current 2I_0. The resulting magnetic field B

at the origin is

Answer 1

Solution

Magnetic field due to loop in xy plane

$\overrightarrow{B_1}=\frac{\mu_0I_0\widehat{z}}{2R}$

Magnetic field due to loop in xz plane

$\overrightarrow{B_2}=\frac{\mu_0 2I_0(-\widehat{y})}{2R}$

Therefore total resultant magnetic field is $\overrightarrow{B}=\overrightarrow{B_1}+\overrightarrow{B_2}$

$\overrightarrow{B}=\frac{\mu_0 I_0((-2\widehat{y})+\widehat{z})}{2R}$