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

Consider two concentric circular coils X and Y, coplanar with vertical plane carrying currents `I_(x)andI_(y)` respectively in anticlockwise and clockwise directions when observed from East to West in above diagram.
For coil-X, magnetic field produced at the common centre O is,
`B_(x)=(mu_(0)N_(x)I_(x))/(2R_(x))`
`thereforeB_(x)=((4pixx10^(_7))(20)(16))/((2)(0.16))`
`thereforeB_(x)=4pixx10^(-4)T" "("Towards East")" "...(1)`
(According to right hand thumb rule)
For coil-Y, magnetic field produced at the common centre O is,
`B_(y)=(mu_(0)N_(y)I_(y))/(2R_(y))`
`thereforeB_(y)=((4pixx10^(-7))(25)(18))/((2)(0.1))`
`thereforeB_(y)=9pixx10^(-4)T" "("Towards West")" "...(2)`
`rArrB_(y)gtB_(x)`
Moreover, `vecB_(y)andvecB_(x)` are colinear and directed in mutually opposite directions. Hence, resultant magnetic field produced at common centre O will be,
`B=B_(y)-B_(x)`
= `9pixx10^(-4)-4pixx10^(-4)`
`B=5pixx10^(-4)T`
`thereforeB=1.57xx10^(-3)T` (Towards West)