Two Concentric circular coils `X` and `Y` of radii `16 cm` and `10cm` lie in the same vertical plane containing `N-S` direction `X` has 20 turns and carries `16A .Y` has `25` truns & carries `18 A.X` has current in anticlockwise direction and `Y` has current in clockwise direction for the observer, looking at the coils facing the west. The magnitude of net magnetic field at their common centre is .

Options

A. `1.6 xx 10^(-5) ` west
B. `1.6 xx 10^(-3) ` east
C. `1.6 xx 10^(-3)` west
D. `1.6 xx 10^(-5) ` east

Answer

C

Explanation

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

Magnetic field at centre due to coil Y .
`B_1 = ( (mu_0I)/(2r) ) xx 25`
`B_1 = [ (4pi xx 10^(-7) xx 18)/(2 xx 10 xx 10^(-2) ) ] xx 25 ox` towards west
`B_1 = 2826 xx 10^(-6) T ox ` west
magnetic field at centre due to coil x
`B_2 = [ (mu_0I)/(2r)] 20 `
` B_2 = [ (4pi xx 10^(-7) xx 16)/(2 xx (16 xx 10^(-2) )] 20 o.` East
At centre of coils
`B_("net") = B_1 - B_2 = 1570 xx 10^(-6) T ox` west
So, a magnetic field nearly `1.6 xx 10^(-3) T` will appear at centre of the circular coil directed towards west .