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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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$\frac{μ_{0} I}{R}$

$\frac{\sqrt{5} μ_{0} I}{2 R}$

$\frac{3 μ_{0} I}{2 R}$

$\frac{μ_{0} I}{2 R}$

answer is B.

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Detailed Solution

The magnetic field (B) at the centre of circular current carrying coil of radius R and current I

$B = \frac{μ_{0} I}{2 R}$ Similarly, if current =2I, then

Magnetic field $= \frac{μ_{0} 2 I}{2 R} = 2 B$
So, resultant magnetic field
$= \sqrt{B^{2} + {(2 B)}^{2}} = \sqrt{5 B^{2}} = \sqrt{5 B}$
$= \frac{μ_{0} I \sqrt{5}}{2 R}$

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