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.

#### Solution

Radius of coil X, *r*_{1} = 16 cm = 0.16 m

Radius of coil Y,* r*_{2} = 10 cm = 0.1 m

Number of turns of on coil X, *n*_{1} = 20

Number of turns of on coil Y, *n*_{2} = 25

Current in coil X, *I*_{1} = 16 A

Current in coil Y, *I*_{2} = 18 A

Magnetic field due to coil X at their centre is given by the relation,

`B_i=(mu_0n_1I_1)/(2r_1)`

Where,

`mu_0` = Permeability of free space = `4pixx10^-7 TmA^-1`

`therefore B_1=(4pixx10^-7xx20xx16)/(2xx0.16)`

`=4pixx10^-4 T "(towards East)"`

Magnetic field due to coil Y at their centre is given by the relation,

`B_2=(mu_0n_2I_2)/(2r_2)`

`=(4pixx10^-7xx25xx18)/(2xx0.10)`

`=9pixx10^-4 T "towards west"`

Hence, net magnetic field can be obtained as:

`B=B_2-B_1`

`=9pixx10^-4-4pixx10^-4`

`=5pixx10^-4 T`

`=1.57xx10^-3 T ("towards west")`