Question

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 :-

• A. $5\pi \times 10^{-4}T$
• B. $7\pi \times 10^{-4}T$
• C. $\pi \times 10^{-4}T$
• D. $9\pi \times 10^{-4}T$

Answer 1

Answer: (A)

Net field at common centre :
${\left(B_0\right)}_{net}=\frac{{\left(\mu \right)}_0}{2}\left[\frac{N_y{I}_y}{R_y}-\frac{N_x{I}_x}{R_x}\right]$

$=\frac{4\pi \times 10^{-7}}{2}\left[\frac{25\times 10}{0.1}-\frac{20\times 16}{0.16}\right]$
$=5\pi \times 10^{-4}T$