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

Options

A. `1.6xx10^(-5)` west
B. `1.6xx10^(-3)` east
C. `1.6xx10^(-3)` west
D. `1.6xx10^(-5)` east

Answer

3

Explanation

The concentric coils are in the plane north to south. Let us decide the directions with convenience in the plane of paper.

Magnetic field at centre due to coil `Y`.
`B_(1)=((mu_(0)I)/(2r))xx25`
`B_(1)=[(4pixx10^(-7)xx18)/(2xx10xx10^(-2))]xx25o x` Towards west
`B_(1)=2826xx10^(-6)To x` west
Magnetic field at centre due to coil `X`
`B_(2)=[(mu_(0)I)/(2r)]`
`B_(2)=[(4pixx10^(-7)xx16)/(2xx(16xx10^(-2)))]20 .` East
At centre of coils
`B_(n et)=B_(1)-B_(2)=1570xx10^(-6)To x` West
So, a magnetic field nearly `1.6xx10^(-3)T` will appear at centre of the circular coil directed towards west.