4.14 Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

Radius of coil X,  r1=16cm=0.16m
Radius of Y, r2=10cm=0.1m
Number of turns on coil X, n1=20
Number of turns on coil Y, n2=25
Current in coil X, I1=16A
Current in coil Y, I2=18A
Magnetic field due to coil X at their centre is given by the relation,
B1=μ0N1I12r1Where, μ0=Permeabilityoffreespace=4π×10-7TmA-1
B1=4π×10-7×20×162×0.16=4π×10-4T(TowardsEast)
Magnetic field due to coil Y at their centre is given by the relation,
B2=μ0N2I22r2
Where, μ0=Permeabilityoffreespace=4π×10-7TmA-1
B1=4π×10-7×25×182×0.10=9π×10-4T(TowardsEast)
Hence, net magnetic field can be obtained as:
B=B2-B1=9π×10-4T-4π×10-4T
=5π×10-4T
=5×3.13×10-4T=1.57×10-3T(TowardsWest)