Question

Two circular coils are concentric and lie in the same plane. The inner coil contains 160 turns of wire, has a radius of 0.012 m, and carries a current of 8.1 A. The outer coil contains 140 turns and has a radius of 0.021 m. What must be the magnitude of the current in the outer coil, such that the net magnetic field at the common center of the two coils is zero?

Answer 1

Apply, B2 = B1

N2*mue*I2/(2*R2) = N1*mue*I1/(2*R1)

140*I2/0.021 = 160*8.1/0.012

I2 = 160*8.1*0.021/(0.012*140)

= 16.2 A

Answer 2

Here ,

Magnetic field at the centre due to a loop is given as

B = N *u0*I/(2R)

Now , balancing both the fields

160*u0*8.1/(2*0.012) = u0*140* I /(2*.021)

I = 16.2 A

the magnitude of the current in the outer coil is 16.2 A