Question #135011
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
1
Expert's answer
2020-09-29T09:44:29-0400

Solution

Magnetic field due to loop in xy plane

B1=μ0I0z^2R\overrightarrow{B_1}=\frac{\mu_0I_0\widehat{z}}{2R}

Magnetic field due to loop in xz plane

B2=μ02I0(y^)2R\overrightarrow{B_2}=\frac{\mu_0 2I_0(-\widehat{y})}{2R}

Therefore total resultant magnetic field is B=B1+B2\overrightarrow{B}=\overrightarrow{B_1}+\overrightarrow{B_2}


B=μ0I0((2y^)+z^)2R\overrightarrow{B}=\frac{\mu_0 I_0((-2\widehat{y})+\widehat{z})}{2R}


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