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

\frac{μ_{0} I}{2 R}

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\frac{μ_{0} I}{R}

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\frac{\sqrt{5} μ_{0} I}{2 R}

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\frac{3 μ_{0} I}{2 R}

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Solution

The correct option is A $\frac{\sqrt{5} μ_{0} I}{2 R}$
Magnetic field at center due to first coil is $B_{1} = \frac{μ_{0} I}{2 R}$
Magnetic field at center due to second coil perpendicular to the first is $B_{2} = \frac{μ_{0} (2 I)}{2 R}$
Hence net magnetic field at the center= $\sqrt{B_{1}^{2} + B_{2}^{2}}$
$= \frac{\sqrt{5} μ_{0} I}{2 R}$

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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

The correct option is A √5μ0I2RMagnetic field at center due to first coil is B1=μ0I2RMagnetic field at center due to second coil perpendicular to the first is B2=μ0(2I)2RHence net magnetic field at the center=√B21+B22=√5μ0I2R