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  4. Two concentric circular coils X and Y of radii 16cm and 10cm, respectively, lie in the same vertical plane containing the north to 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 the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. The magnitude of the net magnetic field due to the coils at their centre is :-

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Q. Two concentric circular coils $X$ and $Y$ of radii $16cm$ and $10cm,$ respectively, lie in the same vertical plane containing the north to 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 the current in $X$ is anticlockwise, and clockwise in $Y,$ for an observer looking at the coils facing west. The magnitude of the net magnetic field due to the coils at their centre is :-

NTA AbhyasNTA Abhyas 2020

Solution:

Net field at common centre :
$\left(B_{0}\right)_{n e t}=\frac{\left(\mu \right)_{0}}{2}\left[\frac{N_{y} I_{y}}{R_{y}} - \frac{N_{x} I_{x}}{R_{x}}\right]$
Solution
$=\frac{4 \pi \times 10^{- 7}}{2}\left[\frac{25 \times 10}{0 . 1} - \frac{20 \times 16}{0 . 16}\right]$
$=5\pi \times 10^{- 4}T$