# Two similar coils of radius r are lying concentrically with their planes at right angles to each others. The currents flowing in them are $I \ and\ 2 I$, respectively. The resultant magnetic field induction at  the centre will be: Option 1) $\frac{\sqrt{5}\mu_{o}I}{2R}$ Option 2) $\frac{{3}\mu_{o}I}{2R}$ Option 3) $\frac{\mu_{o}I}{2R}$ Option 4) $\frac{\mu_{o}I}{R}$

Magnetic field due to cCrcular Current Carrying arc -

$B=\frac{\mu_{o}}{4\pi}\:\frac{2\pi i}{r}=\frac{\mu_{o}i}{2r}$

- wherein

$B_{1}=\frac{\mu _{oI}}{2r } \:\:\:\:\:B=\sqrt{B_{1}^{2}+B_{2}^{2}}=\sqrt{5}\frac{\mu ^oI}{2r}\\ B_{2}=\frac{\mu_{o}.2I}{2r}$

Option 1)

$\frac{\sqrt{5}\mu_{o}I}{2R}$

This option is correct

Option 2)

$\frac{{3}\mu_{o}I}{2R}$

This option is incorrect

Option 3)

$\frac{\mu_{o}I}{2R}$

This option is incorrect

Option 4)

$\frac{\mu_{o}I}{R}$

This option is incorrect

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