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(A) The magnetic field induction at the centre of a circular coil of radius $R$ carrying current $I$ is given by $B = \frac{\mu_{0} I}{2 R}$.For the f

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$\frac{\sqrt{5} \mu_{0} I}{2 R}$

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(A) The magnetic field induction at the centre of a circular coil of radius $R$ carrying current $I$ is given by $B = \frac{\mu_{0} I}{2 R}$.For the first coil with current $I$,the magnetic field is $B_{1} = \frac{\mu_{0} I}{2 R}$.For the second coil with current $2I$,the magnetic field is $B_{2} = \frac{\mu_{0} (2I)}{2 R} = \frac{\mu_{0} I}{R}$.Since the planes of the coils are at right angles to each other,the magnetic fields $B_{1}$ and $B_{2}$ are mutually perpendicular.The resultant magnetic field induction $B_{	ext{net}}$ at the centre is given by:$B_{	ext{net}} = \sqrt{B_{1}^{2} + B_{2}^{2}}$$B_{	ext{net}} = \sqrt{\left(\frac{\mu_{0} I}{2 R}ight)^{2} + \left(\frac{\mu_{0} I}{R}ight)^{2}}$$B_{	ext{net}} = \frac{\mu_{0} I}{2 R} \sqrt{1^{2} + 2^{2}}$$B_{	ext{net}} = \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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