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Question

# 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 2 I, respectively. The resultant magnetic field induction at the centre will be

A
5μ0I2R
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B
3μ0I2R
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C
μ0I2R
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D
μ0IR
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Solution

## The correct option is A √5μ0I2RThe magnetic field, due the coil, carrying current I AmpereB1=μ0I2RThe magnetic field due to the coil, carrying current 2I AmpereB2=μ0(2I)2RThe resultant BBnet=√B21+B22+2B1B2cosθ where θ=90o⇒Bnet=√B21+B22+2B1B2cos900=μ0(2I)2R√1+4=√5μ0I2R

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