Two circular coils are concentric and lie in the same plane. The inner coil cont

Question

Two circular coils are concentric and lie in the same plane. The inner coil contains 120 turns of wire, has a radius of 0.012m,and carries a current of 6.0A. The outer coil contains 150turns and has a radius of 0.017 m. What must be the magnitudeand direction (relative to the current in the inner coil) ofthe current in the outer coil, such that the net magnetic field atthe common center of the two coils is zero?

answer: 6.8A, opposite to the direction of the current in the innercoil

Explanation / Answer

.direction : at first,we can see the direction of the outer coil must beopposite to the direction in the inner coil (in order to thedirection of magnetic force will be opposite also) Magnitude : as we know,the magnetic field at the center of the coil with radiusR and the current I :   B = oI/2R => total magnetic field : B = N1*oI1/2R1 - N2*oI2/2R2 = 0 => N1I1/R1 = N2I2/R2 => I2 = I1*(N1/N2)*(R2/R1) = 6*(120/150)*(0.017/0.012) =6.8 A

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