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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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$\frac{3 μ_{0} I}{2 R}$

$\frac{μ_{0} I}{2 R}$

$\frac{\sqrt{5} μ_{0} I}{2 R}$

$\frac{μ_{0} I}{R}$

answer is A.

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Detailed Solution

$B_{1} = \frac{μ_{0} (I)}{2 R}; B_{2} = \frac{μ_{0} (2 I)}{2 R}$

$B_{net} = \sqrt{B_{1}^{2} + B_{2}^{2}} = \sqrt{{(\frac{μ_{0} I}{2 R})}^{2} + {(\frac{2 μ_{0} I}{2 R})}^{2}}$

$B_{net} = \frac{\sqrt{5} μ_{0} I}{2 R}$

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