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Question

# Two concentric coils each of radius equal to 2π cm are placed in such a manner that their planes are at right angles to each other. Current of 3 A and 4 A respectively are flowing through the coil. What will be the magnetic induction at the center of the loop ?

A
5×105 T
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B
7×105 T
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C
1×105 T
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D
None of these
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Solution

## The correct option is A 5×10−5 T The direction of the magnetic fields due to both the loops is determined by using right-hand thumb rule. Magnetic field due to a loop-B carrying current 4 A is, B1=μ0I2R B1=4π×10−7×42×2π×10−2 ∴B1=4×10−5 T along y−axis So, magnetic field due to loop-A carrying current 3 A is, B2=μ0I2R B2=4π×10−7×32×2π×10−2 ∴B2=3×10−5 T along x−axis So the net magnetic field is given by, −−→Bnet=−→B1+−→B2=B1 ^j+B2 ^i ∴∣∣−−→Bnet∣∣=√|B1|2+|B2|2 Bnet=√(4×10−5)2+(3×10−5)2 ∴Bnet=5×10−5 T Hence, option (a) is correct.

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