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Question

Magnetic field induction due to vertical loop at the centre $O$ is

$B_{1}=\frac{\mu_{0} I}{2 R}$

It acts in horizontal direction.

Magnetic fi

Vedclass · Accepted Answer

$\frac{{\sqrt 5 {\mu _0}I}}{{2R}}$

Vedclass · Answer

Magnetic field induction due to vertical loop at the centre $O$ is

$B_{1}=\frac{\mu_{0} I}{2 R}$

It acts in horizontal direction.

Magnetic field induction due to horizontal loop at the centre $O$ is

$B_{2}=\frac{\mu_{0} 2 I}{2 R}$

It acts in vertically upward direction.

As $B_{1}$ and $B_{2}$ are perpendicular to each other, therefore the resultant magnetic field induction at the centre $O$ is

${B_{	ext {net }}=\sqrt{B_{1}^{2}+B_{2}^{2}}=\sqrt{\left(\frac{\mu_{0} I}{2 R}ight)^{2}+\left(\frac{\mu_{0} 2 I}{2 R}ight)^{2}}}$

${B_{	ext {net }}=\frac{\mu_{0} I}{2 R} \sqrt{(1)^{2}+(2)^{2}}=\frac{\sqrt{5} \mu_{0} I}{2 R}}$

Two similar coils of radius $R$ are lying concentrically with their planes at right angles to each other. The currents flowing in them are $I$ and $2I$, respectively. The resultant magnetic field induction at the centre will be

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