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.

Explanation

For coil X Radius of coil, `r_(x)=16 cm =0.16 m` ltbr No. of turns `n_(x)=20`
Current in the coil `I_(x)=16 A` (Anti clockwise) For coil Y
Radius of coil, `r_(y)=10 cm =0.1m`
No. of turns `n_(y)=25`
Current in the coil `I_(y) = 18 A` (clockwise) The magnitude of the magnetic field at the centre of coil X
`B_(x)=(mu_(0))/(4pi).(2I_(x).pi n_(x))/(r_(x))=(10^(-7)xx2xx16xx3.14xx20)/(0.16)T`
`B_(x)=4pi xx10^(-4) T`
The magnitude of magnetic flux at the centre of coil Y
`B_(y)=(mu_(0))/(4pi).(2pi I_(y). n_(y))/(r_(y))=(10^(-7)xx2xxpixx18xx25)/(0.1)=9pi xx10^(-4) T`
Net magnitude field at the centre `B=B_(y)-B_(x)`
`=(9pi - 4pi)xx10^(-4)=5pi xx10^(-4)`
`=1.6xx10^(-3) T` (towards west).