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Question

# Two concentric coils each of radius equal to 2π cm are placed right angles to each other. If 3A and 4A are the currents flowing through the two coils respectively. The magnetic induction (in Wb m−2) at the centre of the coils will be

A
12×105
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B
105
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C
5×105
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D
7×105
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Solution

## The correct option is D 5×10−5As the two concentric coils are placed at right angle to each other, thus the magnetic induction at centre of respective coils are also at right angle. Let say, magnetic induction due to coil 1 points in x direction and that of coil 2 points in y direction.Given : r1=r2=2π cm =0.02π m I1=3A I2=4AMagnetic induction due to coil 1, B1=μoI12r1 ^i∴ B1=4π×10−7×3(2)(0.02π)=3×10−5 ^i Wb/m2 Magnetic induction due to coil 2, B2=μoI22r2 ^j∴ B2=4π×10−7×4(2)(0.02π)=4×10−5 ^j Wb/m2Thus total magnetic induction BT=√B21+B22∴ BT=√32+42×10−5=5×10−5 Wb/m2

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